Understand what perimeter means — the distance around a closed shape
Understand what area means — the surface covered by a closed shape
Find the perimeter of rectangles using the formula P = 2(l + b)
Find the perimeter of squares using the formula P = 4 × side
Find the perimeter of triangles by adding all three sides
Find the area of rectangles using A = l × b
Find the area of squares using A = side × side
Find the area of right triangles using A = ½ × base × height
Find perimeter and area of composite shapes (L-shapes, T-shapes)
Solve word problems involving perimeter and area in real-life Indian contexts
Introduction — Perimeter and Area in Real Life
Look around you — everything has a shape! The floor of your room, the pages of your notebook, the school playground, a cricket ground. Two important measurements help us understand these shapes: Perimeter and Area.
Perimeter tells us the distance around a shape — like the length of fencing needed to go around a garden, or the length of lace needed to put a border on a saree.
Area tells us the surface covered by a shape — like how many tiles you need to cover a floor, or how much paint is needed to colour a wall.
Here are some real-life examples:
Fencing a garden — you need to know the perimeter
Laying tiles on a floor — you need to know the area
Painting a wall — you need to know the area
Putting a border on a photo frame — you need the perimeter
Buying carpet for a room — you need the area
Running around a playground — you cover the perimeter
Putting lace around a tablecloth — you need the perimeter
What is Perimeter?
The perimeter of a closed shape is the total distance around it. If you walk along the boundary of a shape and come back to where you started, the total distance you walk is the perimeter.
Definition
Perimeter = Sum of all sides of a closed shape
Unit: Same as length — centimetres (cm), metres (m), kilometres (km)
To find the perimeter of any shape, simply add up the lengths of all its sides.
Example 1: Find the perimeter of a shape with sides 5 cm, 3 cm, 7 cm, and 4 cm.
Perimeter = 5 + 3 + 7 + 4 = 19 cm
Example 2: Meena wants to put a ribbon border around a triangular card with sides 12 cm, 9 cm, and 15 cm. How much ribbon does she need?
Perimeter = 12 + 9 + 15 = 36 cm
Meena needs 36 cm of ribbon.
Image needed: A visual showing a person (child) walking around the boundary of a rectangular park. Arrows showing the direction of walking along all four sides. Labels "Perimeter = distance walked around the shape". A second small image showing the inside of the shape coloured/shaded, labelled "Area = surface covered inside". Style: Split illustration — left side shows perimeter concept (walking around), right side shows area concept (surface coloured). Bright, child-friendly, flat illustration. Size: 750×400px
Perimeter of a Rectangle
A rectangle has 4 sides — two lengths and two breadths. The opposite sides are equal.
Formula: Perimeter of a Rectangle
P = length + breadth + length + breadth
P = 2 × length + 2 × breadth
P = 2 × (length + breadth)
P = 2(l + b)
Image needed: A rectangle with length and breadth clearly labelled. Length marked on top and bottom sides (e.g., 8 cm), breadth marked on left and right sides (e.g., 5 cm). Formula P = 2(l + b) shown below. Arrows tracing the perimeter around all 4 sides. Style: Clean geometric diagram, blue rectangle with black labels, formula in a box below Size: 500×350px
Example 1: Find the perimeter of a rectangle with length = 12 cm and breadth = 7 cm.
P = 2(l + b)
P = 2(12 + 7)
P = 2 × 19
P = 38 cm
Example 2: A rectangular garden has length 25 m and breadth 18 m. Arjun wants to put a fence around it. Find the total length of fencing needed.
P = 2(l + b)
P = 2(25 + 18)
P = 2 × 43
P = 86 m
Arjun needs 86 metres of fencing.
Example 3: The perimeter of a rectangular field is 120 m. If its length is 40 m, find its breadth.
P = 2(l + b)
120 = 2(40 + b)
120 ÷ 2 = 40 + b
60 = 40 + b
b = 60 − 40
b = 20 m
Example 4: Dhruv wants to put a golden border (lace) around a rectangular photo frame that is 30 cm long and 20 cm wide. If the lace costs ₹5 per cm, find the total cost.
P = 2(l + b) = 2(30 + 20) = 2 × 50 = 100 cm
Cost = 100 × ₹5 = ₹500
Perimeter of a Square
A square has 4 equal sides. Since all sides are the same, the formula is simpler.
Formula: Perimeter of a Square
P = side + side + side + side
P = 4 × side
P = 4s
Example 1: Find the perimeter of a square with side = 9 cm.
P = 4 × side
P = 4 × 9
P = 36 cm
Example 2: A square playground has a side of 50 m. Akriti runs around it 3 times every morning. What total distance does she run?
Perimeter = 4 × 50 = 200 m
Distance for 3 rounds = 200 × 3 = 600 m
Example 3: The perimeter of a square napkin is 64 cm. Find the length of each side.
P = 4 × side
64 = 4 × side
side = 64 ÷ 4
side = 16 cm
Example 4: A square park has a perimeter of 480 m. If fencing costs ₹75 per metre, find the total cost of fencing the park.
Total cost = Perimeter × Cost per metre
Total cost = 480 × ₹75 = ₹36,000
Perimeter of a Triangle
A triangle has 3 sides. To find its perimeter, add all three sides together.
Formula: Perimeter of a Triangle
P = side₁ + side₂ + side₃
P = a + b + c (where a, b, c are the three sides)
Example 1: Find the perimeter of a triangle with sides 6 cm, 8 cm, and 10 cm.
P = 6 + 8 + 10 = 24 cm
Example 2 (Equilateral Triangle): All sides of an equilateral triangle are equal. If each side = 14 cm, find the perimeter.
P = 3 × side = 3 × 14 = 42 cm
Example 3 (Isosceles Triangle): An isosceles triangle has two equal sides of 10 cm each and a base of 12 cm. Find the perimeter.
P = 10 + 10 + 12 = 32 cm
Example 4: A triangular garden has sides 15 m, 20 m, and 25 m. Ravi wants to plant hedges along its boundary. Find the total length of hedges needed.
P = 15 + 20 + 25 = 60 m
Think About It: An equilateral triangle has all 3 sides equal, so P = 3 × side. An isosceles triangle has 2 sides equal, so P = 2 × equal side + base. A scalene triangle has all 3 sides different, so you must add all three individually.
What is Area?
The area of a shape is the amount of flat surface it covers. Think of it as how many square tiles of a fixed size can fit inside the shape without gaps or overlaps.
Definition
Area = The amount of surface enclosed by a closed shape
We use square units because area is measured by counting unit squares
Counting Squares on Grid Paper
The simplest way to find area is to count the number of unit squares inside a shape drawn on grid paper. Each small square on the grid = 1 square unit (1 sq. cm or 1 cm²).
Image needed: A grid paper (squared paper) with three shapes drawn on it: (1) a 4×3 rectangle with all 12 squares coloured in blue, labelled "Area = 12 sq. cm", (2) a 3×3 square with 9 squares coloured in green, labelled "Area = 9 sq. cm", (3) an irregular shape made of squares with each square numbered, showing the counting method. Style: Clean grid illustration with coloured squares, numbers inside each square, clear labels Size: 700×400px
Example: On a grid paper, a rectangle covers 5 squares along the length and 3 squares along the breadth. What is its area?
Area = Number of unit squares = 5 × 3 = 15 square cm (15 cm²)
Think About It: Why do we say "square centimetres" and not just "centimetres"? Because area measures a 2-dimensional surface (length × breadth), not just a 1-dimensional line. The word "square" reminds us that we are measuring in two directions!
Area of a Rectangle
Instead of counting squares every time, we use a formula. For a rectangle, the area equals the number of rows times the number of columns — which is length times breadth.
Formula: Area of a Rectangle
Area = length × breadth
A = l × b
Unit: square cm (cm²), square m (m²), etc.
Example 1: Find the area of a rectangle with length = 14 cm and breadth = 9 cm.
A = l × b
A = 14 × 9
A = 126 cm²
Example 2: A classroom is 10 m long and 8 m wide. Find its area.
A = l × b = 10 × 8 = 80 m²
Example 3: Priya's room is 5 m long and 4 m wide. She wants to lay tiles on the floor. Each tile covers 1 m². How many tiles does she need?
Area of room = 5 × 4 = 20 m²
Number of tiles = 20 ÷ 1 = 20 tiles
Example 4: A rectangular plot has an area of 540 m². If its length is 30 m, find its breadth.
A = l × b
540 = 30 × b
b = 540 ÷ 30
b = 18 m
Example 5: The floor of a hall is 20 m long and 15 m wide. If laying carpet costs ₹120 per square metre, find the total cost.
Area = 20 × 15 = 300 m²
Cost = 300 × ₹120 = ₹36,000
Area of a Square
A square has all four sides equal. So the area is simply side multiplied by itself.
Formula: Area of a Square
Area = side × side
A = s × s = s²
(We read s² as "s squared" or "side squared")
Example 1: Find the area of a square with side = 11 cm.
A = s × s = 11 × 11 = 121 cm²
Example 2: A square park has a side of 45 m. Find its area.
A = 45 × 45 = 2,025 m²
Example 3: A square chess board has an area of 400 cm². Find the length of each side.
A = side × side
400 = side × side
side = √400 = 20 cm
(Because 20 × 20 = 400)
Example 4: Hridan wants to cover a square table-top of side 60 cm with decorative paper. If the paper costs ₹2 per cm², what is the total cost?
A right triangle is exactly half of a rectangle. If you draw a diagonal in a rectangle, you get two equal right triangles. This is why the area of a right triangle is half the area of the rectangle formed by its base and height.
Formula: Area of a Right Triangle
Area = ½ × base × height
A = ½ × b × h
The base and height are the two sides that form the right angle (90°)
Image needed: A rectangle divided by a diagonal into two right triangles. The rectangle is labelled with base and height. One triangle is shaded (coloured). Below it, the same right triangle shown separately with base and height labelled, and the formula A = ½ × b × h. An annotation showing "Rectangle area = b × h" and "Triangle area = ½ × b × h (half of rectangle)". Style: Clean geometric diagram, blue rectangle, one triangle shaded orange, clear labels and arrows Size: 650×400px
Example 1: Find the area of a right triangle with base = 10 cm and height = 6 cm.
A = ½ × b × h
A = ½ × 10 × 6
A = ½ × 60
A = 30 cm²
Example 2: A right triangle has base = 15 cm and height = 8 cm. Find its area.
A = ½ × 15 × 8 = ½ × 120 = 60 cm²
Example 3: The area of a right triangle is 36 cm². If its base is 12 cm, find its height.
A = ½ × b × h
36 = ½ × 12 × h
36 = 6 × h
h = 36 ÷ 6
h = 6 cm
Example 4: A triangular piece of land has a right angle. Its base is 20 m and height is 14 m. Find its area.
A = ½ × 20 × 14 = ½ × 280 = 140 m²
Think About It: If a rectangle has area = 48 cm², and you cut it diagonally into two right triangles, what is the area of each triangle? Each triangle has area = 48 ÷ 2 = 24 cm². That is exactly ½ × base × height!
Relationship: Perimeter vs Area
An important concept: shapes with the same perimeter can have different areas, and shapes with the same area can have different perimeters!
Same Perimeter, Different Area
Example: Consider two rectangles, both with perimeter = 24 cm:
Rectangle A: length = 10 cm, breadth = 2 cm
Perimeter = 2(10 + 2) = 24 cm ✓
Area = 10 × 2 = 20 cm²
Rectangle B: length = 7 cm, breadth = 5 cm
Perimeter = 2(7 + 5) = 24 cm ✓
Area = 7 × 5 = 35 cm²
Both have the same perimeter (24 cm), but Rectangle B has a larger area! The closer a rectangle is to being a square, the larger its area for the same perimeter.
Same Area, Different Perimeter
Example: Consider two rectangles, both with area = 36 cm²:
Rectangle P: length = 18 cm, breadth = 2 cm
Area = 18 × 2 = 36 cm² ✓
Perimeter = 2(18 + 2) = 40 cm
Rectangle Q: length = 6 cm, breadth = 6 cm (a square!)
Area = 6 × 6 = 36 cm² ✓
Perimeter = 2(6 + 6) = 24 cm
Both have the same area (36 cm²), but Rectangle P has a much larger perimeter! A square gives the smallest perimeter for a given area.
Think About It: If a farmer has 40 m of fencing wire, what shape should the field be to get the maximum area? Answer: A square! A 10 m × 10 m square gives area = 100 m², which is more than any other rectangle with perimeter 40 m.
Composite Shapes (L-Shapes, T-Shapes)
Composite shapes are made by combining two or more simple shapes (usually rectangles). To find their perimeter and area, we break them into simpler parts.
Strategy for Composite Shapes
Perimeter: Add up all the outer sides (walk around the outside edge)
Area: Break the shape into rectangles, find the area of each, then add them together
Image needed: An L-shaped figure with all dimensions clearly labelled. The shape is divided into two rectangles by a dashed line. Rectangle 1 is coloured blue, Rectangle 2 is coloured green. The formula shows: Total Area = Area of Rectangle 1 + Area of Rectangle 2. All outer sides are marked with their lengths in cm. Style: Clean geometric diagram, two-colour scheme for the two parts, all measurements clearly labelled Size: 600×450px
Example 1 (L-Shape): Find the perimeter and area of the following L-shaped figure:
The L-shape has outer dimensions: Total length = 10 cm (vertical), Total width = 8 cm (horizontal).
The step (cut-out) is 4 cm × 3 cm from the top-right corner.
So the shape has sides: 10, 8, 4, 3, 6, 5 (going around clockwise).
Wait — let us label carefully:
Bottom = 8 cm, Left side = 10 cm, Top-left = 5 cm (going right), Step-down = 4 cm, Step-right = 3 cm, Right side = 6 cm
Perimeter = 8 + 10 + 5 + 4 + 3 + 6 = 36 cm
Area: Break into two rectangles:
Rectangle 1 (bottom): 8 cm × 6 cm = 48 cm²
Rectangle 2 (top-left): 5 cm × 4 cm = 20 cm²
Total Area = 48 + 20 = 68 cm²
Example 2 (L-Shape — easier): An L-shaped room has these dimensions:
Outer length = 12 m, outer width = 9 m. A 5 m × 4 m rectangular piece is removed from one corner.
Area = Area of full rectangle − Area of removed piece
= (12 × 9) − (5 × 4)
= 108 − 20
= 88 m²
Perimeter: Walk around the outside edge.
= 12 + 9 + 7 + 4 + 5 + 5 = ... (You need to calculate missing sides carefully based on given dimensions.)
Example 3 (T-Shape): A T-shaped cardboard has:
Top bar: 16 cm wide × 4 cm tall
Vertical stem: 6 cm wide × 10 cm tall
Perimeter: Walk around the outside:
Top = 16, right step-down = 4, right horizontal = 5 (toward centre), vertical stem right = 10, bottom = 6, vertical stem left = 10, left horizontal = 5, left step-up = 4
P = 16 + 4 + 5 + 10 + 6 + 10 + 5 + 4 = 60 cm
Think About It: When finding the area of composite shapes, you can either (1) break the shape into parts and add their areas, or (2) find the area of the full rectangle and subtract the "missing" piece. Both methods give the same answer!
Word Problems — Indian Context
Problem 1: A rectangular school playground is 80 m long and 50 m wide. The school wants to put a wire fence around it. If the wire costs ₹45 per metre, what is the total cost?
Problem 3: A rectangular garden is 35 m long and 20 m wide. Find: (a) the cost of fencing it at ₹60 per metre, and (b) the cost of planting grass at ₹25 per square metre.
(b) Area = 35 × 20 = 700 m²
Cost of planting = 700 × ₹25 = ₹17,500
Problem 4: Arjun's room is 6 m long and 5 m wide. He wants to lay square tiles of side 50 cm on the floor. How many tiles will he need?
Solution:
First, convert all measurements to the same unit (cm):
Room: 600 cm × 500 cm
Area of room = 600 × 500 = 3,00,000 cm²
Area of one tile = 50 × 50 = 2,500 cm²
Number of tiles = 3,00,000 ÷ 2,500 = 120 tiles
Problem 5: A farmer has a rectangular field that is 200 m long and 150 m wide. He leaves a 5 m wide path around the inside of the field. What is the area of the path?
Solution:
Area of full field = 200 × 150 = 30,000 m²
Inner field (without path): length = 200 − 5 − 5 = 190 m, breadth = 150 − 5 − 5 = 140 m
Area of inner field = 190 × 140 = 26,600 m²
Area of path = 30,000 − 26,600 = 3,400 m²
Problem 6: Kavitha is putting a golden border (zari) around a square saree piece of side 1.2 m. If the zari costs ₹150 per metre, what is the total cost?
The total distance around a closed shape (sum of all sides)
Area
The amount of flat surface enclosed by a closed shape
Length (l)
The longer side of a rectangle
Breadth (b)
The shorter side of a rectangle (also called width)
Side (s)
The length of one side of a square
Base
The bottom side of a triangle (or any side chosen as reference)
Height
The perpendicular distance from base to the opposite vertex
Square units
Units for measuring area: cm², m², km²
Composite shape
A shape made by combining two or more simple shapes
Right triangle
A triangle with one angle equal to 90°
Equilateral triangle
A triangle with all three sides equal
Isosceles triangle
A triangle with two sides equal
Key Points to Remember
Perimeter of a Rectangle: P = 2(l + b)
Perimeter of a Square: P = 4 × side
Perimeter of a Triangle: P = a + b + c (sum of all sides)
Area of a Rectangle: A = l × b
Area of a Square: A = side × side = s²
Area of a Right Triangle: A = ½ × base × height
Perimeter is measured in linear units (cm, m, km)
Area is measured in square units (cm², m², km²)
Same perimeter does NOT mean same area (and vice versa)
For composite shapes: break into rectangles, find area of each part, then add
Always check that all measurements are in the same unit before calculating
A square has the largest area for a given perimeter among all rectangles
Finished learning? Now test what you know!
🎯 Quick Quiz — Test Yourself!
Answer these questions right here. You get instant feedback — no paper needed!
Score: 0 / 8
1. Perimeter is the:
Perimeter = total distance around the boundary of a shape.
2. The area of a rectangle is found by:
Area of rectangle = length × breadth.
3. A square has side 5 cm. Its perimeter is:
Perimeter of square = 4 × side = 4 × 5 = 20 cm.
4. A square has side 5 cm. Its area is:
Area of square = side × side = 5 × 5 = 25 sq cm.
5. A rectangle is 8 cm long and 4 cm wide. Find its perimeter in cm (digits only):
Perimeter = 2 × (8 + 4) = 2 × 12 = 24 cm.
6. A rectangle is 8 cm long and 4 cm wide. Find its area in sq cm (digits only):
Area = length × breadth = 8 × 4 = 32 sq cm.
7. A square field has side 9 m. What is its perimeter in metres? (digits only)
Perimeter = 4 × 9 = 36 m.
8. A square garden has side 10 m. What is its area in square metres? (digits only)
Area = 10 × 10 = 100 sq m.
Practice Questions
A. Find the perimeter of the following rectangles:
1. Length = 15 cm, Breadth = 9 cm. Perimeter =
2. Length = 22 m, Breadth = 14 m. Perimeter =
3. Length = 35 cm, Breadth = 20 cm. Perimeter =
4. Length = 48 m, Breadth = 25 m. Perimeter =
5. Length = 100 m, Breadth = 60 m. Perimeter =
B. Find the perimeter of the following squares:
1. Side = 13 cm. Perimeter =
2. Side = 25 m. Perimeter =
3. Side = 40 cm. Perimeter =
4. Side = 75 m. Perimeter =
C. Find the area of the following rectangles:
1. Length = 12 cm, Breadth = 8 cm. Area =
2. Length = 18 m, Breadth = 11 m. Area =
3. Length = 25 cm, Breadth = 16 cm. Area =
4. Length = 40 m, Breadth = 30 m. Area =
5. Length = 55 cm, Breadth = 20 cm. Area =
D. Find the area of the following squares:
1. Side = 9 cm. Area =
2. Side = 15 m. Area =
3. Side = 22 cm. Area =
4. Side = 50 m. Area =
E. Find the area of the following right triangles:
1. Base = 8 cm, Height = 6 cm. Area =
2. Base = 12 m, Height = 9 m. Area =
3. Base = 20 cm, Height = 15 cm. Area =
4. Base = 14 m, Height = 10 m. Area =
F. Composite Shapes — Find the perimeter and area:
1. An L-shaped room has outer dimensions 12 m × 10 m. A 4 m × 5 m piece is cut from one corner. Find the area of the room.
2. A T-shaped cardboard: top bar is 20 cm × 5 cm, vertical stem is 8 cm × 12 cm. Find the total area.
3. A cross-shaped figure is made from 5 squares, each of side 4 cm (one in centre, one on each side). Find the total area and perimeter.
G. Fill in the blanks:
1. Perimeter of a rectangle = 2 × ( + )
2. Area of a square with side 7 cm = cm²
3. If the perimeter of a square is 48 cm, its side = cm
4. Area of a right triangle with base 10 cm and height 8 cm = cm²
5. A rectangle has length 20 m and perimeter 70 m. Its breadth = m
H. Choose the correct answer (MCQ):
1. The perimeter of a rectangle with length 12 cm and breadth 8 cm is:
a) 96 cmb) 40 cmc) 20 cmd) 80 cm
2. The area of a square with side 6 cm is:
a) 24 cm²b) 36 cm²c) 12 cm²d) 48 cm²
3. Which unit is used to measure area?
a) cmb) mc) cm²d) km
4. A right triangle with base 6 cm and height 4 cm has area:
a) 24 cm²b) 10 cm²c) 12 cm²d) 48 cm²
I. Word Problems:
1. A rectangular park is 120 m long and 80 m wide. Find the cost of fencing it at ₹55 per metre.
2. Sita wants to tile her rectangular kitchen floor that is 4 m long and 3 m wide. Each tile is a square with side 25 cm. How many tiles will she need?
3. A square garden has a side of 30 m. Find: (a) the cost of fencing at ₹40 per metre, and (b) the cost of laying grass at ₹15 per m².
4. A school playground is 60 m long and 40 m wide. Ravi runs around it 5 times every morning. What total distance does he run?
5. Meena wants to put a decorative border around a rectangular photo frame that is 40 cm long and 30 cm wide. If the border strip costs ₹3 per cm, find the total cost.
6. A triangular piece of land has sides 30 m, 40 m, and 50 m. It has a right angle between the 30 m and 40 m sides. Find: (a) its perimeter, and (b) its area.
Activity — Design Your Dream Room!
Take a sheet of graph paper (squared paper). Each small square = 1 metre.
Draw a rectangular room of your choice (e.g., 6 m × 5 m).
Calculate the perimeter of your room. This tells you how much border tape you need for the walls.
Calculate the area of your room. This tells you how much carpet you need for the floor.
Now draw furniture inside: a bed (2 m × 1.5 m), a study table (1 m × 0.5 m), a cupboard (1.5 m × 0.5 m).
Calculate the area of each piece of furniture.
Subtract the furniture areas from the room area to find the free floor space.
Bonus Challenge: Design an L-shaped room on graph paper and calculate its perimeter and area!
Want to review the lesson again?
Mathematics
Perimeter and Area
Class 5 | CBSE / NCERT / ICSE
Name: Class: Date:
Learning Objectives
Find perimeter of rectangles (P = 2(l+b)), squares (P = 4s), and triangles (P = a+b+c)
Find area of rectangles (A = l×b), squares (A = s²), and right triangles (A = ½×b×h)
Find perimeter and area of composite shapes (L-shapes, T-shapes)
Solve word problems involving perimeter and area
What is Perimeter?
Perimeter = The total distance around a closed shape (sum of all sides).
Unit: cm, m, km (same as length). Real-life: Fencing a garden, putting a border on a frame, running around a playground.
[Image: Person walking around a rectangular park (perimeter) vs surface coloured inside (area)]
Perimeter of a Rectangle
Formula: P = 2 × (length + breadth) = 2(l + b)
[Image: Rectangle with length and breadth labelled, formula P = 2(l+b) shown]
Ex 1: l = 12 cm, b = 7 cm → P = 2(12+7) = 2×19 = 38 cm Ex 2: Garden: l = 25 m, b = 18 m → P = 2(25+18) = 2×43 = 86 m of fencing Ex 3: P = 120 m, l = 40 m → 120 = 2(40+b) → 60 = 40+b → b = 20 m Ex 4: Photo frame: l=30cm, b=20cm, lace ₹5/cm → P=2(30+20)=100cm → Cost = 100×5 = ₹500
Perimeter of a Square
Formula: P = 4 × side = 4s
Ex 1: side = 9 cm → P = 4×9 = 36 cm Ex 2: Playground side=50m, Akriti runs 3 rounds → P=200m, total = 200×3 = 600 m Ex 3: P = 64 cm → side = 64÷4 = 16 cm
Perimeter of a Triangle
Formula: P = side₁ + side₂ + side₃ = a + b + c
Ex 1: Sides 6, 8, 10 cm → P = 6+8+10 = 24 cm Ex 2 (Equilateral): All sides = 14 cm → P = 3×14 = 42 cm Ex 3 (Isosceles): Two sides = 10 cm, base = 12 cm → P = 10+10+12 = 32 cm
What is Area?
Area = The amount of flat surface enclosed by a shape.
Unit: cm² (sq cm), m² (sq m), km² (sq km). Real-life: Tiling a floor, painting a wall, buying carpet.
[Image: Grid paper with shapes — rectangle (12 squares), square (9 squares), showing area counting]
Area of a Rectangle
Formula: A = length × breadth = l × b
Ex 1: l = 14 cm, b = 9 cm → A = 14×9 = 126 cm² Ex 2: Room 5m × 4m, 1m² tiles → A = 20 m², need 20 tiles Ex 3: A = 540 m², l = 30 m → b = 540÷30 = 18 m Ex 4: Hall 20m×15m, carpet ₹120/m² → A=300m², cost = 300×120 = ₹36,000
Area of a Square
Formula: A = side × side = s²
Ex 1: side = 11 cm → A = 11×11 = 121 cm² Ex 2: Park side = 45 m → A = 45×45 = 2,025 m² Ex 3: A = 400 cm² → side = √400 = 20 cm (since 20×20=400)
Area of a Right Triangle
Formula: A = ½ × base × height = ½ × b × h
A right triangle is exactly half of a rectangle. The two sides forming the right angle are the base and height.
[Image: Rectangle split diagonally — one triangle shaded, showing A = ½ × b × h is half of rectangle area]
Ex 1: b = 10 cm, h = 6 cm → A = ½×10×6 = ½×60 = 30 cm² Ex 2: b = 15 cm, h = 8 cm → A = ½×15×8 = ½×120 = 60 cm² Ex 3: A = 36 cm², b = 12 cm → 36 = ½×12×h → 36 = 6h → h = 6 cm
Perimeter vs Area — Important!
Remember: Same perimeter ≠ same area. Same area ≠ same perimeter. Ex: P=24cm: Rect 10×2 has area 20cm², Rect 7×5 has area 35cm² (same P, different A!) Ex: A=36cm²: Rect 18×2 has P=40cm, Square 6×6 has P=24cm (same A, different P!)
Composite Shapes (L-Shapes, T-Shapes)
Strategy: Perimeter = add all outer sides. Area = break into rectangles and add areas.
[Image: L-shaped figure divided into two rectangles with dimensions labelled]
L-Shape: Outer 12m×9m, 5m×4m removed → A = (12×9)−(5×4) = 108−20 = 88 m² T-Shape: Top bar 16×4 + stem 6×10 → A = 64+60 = 124 cm², P = 16+4+5+10+6+10+5+4 = 60 cm
Key Words
Term
Meaning
Perimeter
Total distance around a shape (sum of all sides)
Area
Amount of surface enclosed by a shape
Length / Breadth
The two different sides of a rectangle
Base / Height
The two sides forming the right angle in a triangle
Square units
cm², m², km² — units for measuring area
Composite shape
A shape made by combining simple shapes
Key Points:
• P(rectangle) = 2(l+b) | P(square) = 4s | P(triangle) = a+b+c
• A(rectangle) = l×b | A(square) = s² | A(right triangle) = ½×b×h
• Perimeter → linear units (cm, m) | Area → square units (cm², m²)
• Same perimeter ≠ same area (and vice versa)
• Composite shapes: break into rectangles, add areas
• Always use same units before calculating
Practice Questions
A. Find the perimeter of the following rectangles:
1. l = 15 cm, b = 9 cm → P =
2. l = 22 m, b = 14 m → P =
3. l = 35 cm, b = 20 cm → P =
4. l = 48 m, b = 25 m → P =
5. l = 100 m, b = 60 m → P =
B. Find the perimeter of the following squares:
1. Side = 13 cm → P =
2. Side = 25 m → P =
3. Side = 40 cm → P =
4. Side = 75 m → P =
C. Find the area of the following rectangles:
1. l = 12 cm, b = 8 cm → A =
2. l = 18 m, b = 11 m → A =
3. l = 25 cm, b = 16 cm → A =
4. l = 40 m, b = 30 m → A =
5. l = 55 cm, b = 20 cm → A =
D. Find the area of the following squares:
1. Side = 9 cm → A =
2. Side = 15 m → A =
3. Side = 22 cm → A =
4. Side = 50 m → A =
E. Find the area of the following right triangles:
1. Base = 8 cm, Height = 6 cm → A =
2. Base = 12 m, Height = 9 m → A =
3. Base = 20 cm, Height = 15 cm → A =
4. Base = 14 m, Height = 10 m → A =
F. Composite Shapes:
1. L-shaped room: outer 12m×10m, cut-out 4m×5m. Area =
2. T-shaped cardboard: top 20cm×5cm, stem 8cm×12cm. Total area =
3. Cross of 5 squares (side 4cm each). Area = , Perimeter =
G. Fill in the blanks:
1. Perimeter of a rectangle = 2 × ( + )
2. Area of a square with side 7 cm = cm²
3. If perimeter of a square is 48 cm, its side = cm
4. Area of right triangle (base 10 cm, height 8 cm) = cm²
5. Rectangle: l = 20 m, P = 70 m → breadth = m
H. Choose the correct answer (MCQ):
1. Perimeter of rectangle (l=12cm, b=8cm):
a) 96 cmb) 40 cmc) 20 cmd) 80 cm
2. Area of square (side=6cm):
a) 24 cm²b) 36 cm²c) 12 cm²d) 48 cm²
3. Which unit is used for area?
a) cmb) mc) cm²d) km
4. Right triangle (b=6cm, h=4cm) area:
a) 24 cm²b) 10 cm²c) 12 cm²d) 48 cm²
I. Word Problems:
1. A rectangular park is 120 m long and 80 m wide. Find cost of fencing at ₹55/m.
2. Sita's kitchen: 4m × 3m. Tiles are 25cm squares. How many tiles needed?
3. Square garden (side 30m). (a) Fencing cost at ₹40/m. (b) Grass cost at ₹15/m².
4. Playground 60m × 40m. Ravi runs around it 5 times. Total distance?