Mathematics -- Class 4

Topic: Geometry (3D Shapes, Perimeter, and Area)
Name: ____________________________Class: 4Date: ________________
Learning Objectives
A Friendly Introduction

In Class 3, you learned about flat shapes like squares, rectangles, and circles. These are called 2D shapes because they have only length and width.

Now look around you -- a dice, a cricket ball, a chalk box, a cold drink can. These are 3D shapes because they have length, width, and height. In Class 4, we will also learn how to measure the boundary (perimeter) and the space inside (area) of flat shapes.

3D Shapes -- Faces, Edges, and Vertices

A face is a flat surface of a 3D shape. An edge is where two faces meet. A vertex (plural: vertices) is a corner point.

ShapeReal-Life ExampleFacesEdgesVertices
CubeDice, sugar cube6128
CuboidBrick, chalk box6128
SphereCricket ball, globe1 (curved)00
CylinderTin can, pipe3 (2 flat + 1 curved)20
ConeIce cream cone, joker cap2 (1 flat + 1 curved)11

Think: A cube has all faces as squares. How is a cuboid different from a cube?

Perimeter of Rectangle and Square

The perimeter is the total length of the boundary of a shape. We measure it in cm, m, or km.

Perimeter of a Rectangle = 2 x (Length + Breadth)

Example 1: A garden is 15 m long and 10 m wide. Find its perimeter.

Perimeter = 2 x (15 + 10) = 2 x 25 = 50 m

Perimeter of a Square = 4 x Side

Example 2: A carrom board has a side of 74 cm. Find its perimeter.

Perimeter = 4 x 74 = 296 cm

Think: If you walk around a rectangular park that is 200 m long and 100 m wide, how far do you walk in one round?

Introduction to Area

The area is the amount of space inside a flat shape. We can find the area by counting the number of unit squares that fit inside the shape.

Example 3: Counting Squares

If a rectangle is drawn on a grid and it covers 3 rows of 4 squares each, the area = 3 x 4 = 12 square units.

Example 4: A square shape covers 5 rows of 5 squares each on a grid.

Area = 5 x 5 = 25 square units.

Think: Two shapes can have the same area but different perimeters. Can you imagine how?

Key Words
WordMeaning
FaceA flat or curved surface of a 3D shape
EdgeThe line where two faces of a 3D shape meet
VertexA corner point of a 3D shape
PerimeterThe total length of the boundary of a shape
AreaThe space inside a flat shape, measured in square units

Mathematics -- Class 4 (continued)

Topic: Geometry -- Key Points and Practice
Key Points to Remember
Practice Questions

A. Fill in the Blanks

  1. A cube has faces, edges, and vertices.
  2. A sphere has edges and vertices.
  3. The perimeter of a rectangle with length 12 cm and breadth 8 cm is cm.
  4. The perimeter of a square with side 9 cm is cm.
  5. Area is measured in units.

B. Name the 3D Shape

  1. A shape like a cricket ball:
  2. A shape like a matchbox:
  3. A shape like an ice cream cone:
  4. A shape like a water pipe:

C. Find the Perimeter

  1. A rectangle with length 20 m and breadth 14 m. Perimeter = m
  2. A square with side 25 cm. Perimeter = cm
  3. A rectangular field is 50 m long and 30 m wide. Perimeter = m

D. Multiple Choice Questions

  1. How many faces does a cylinder have?
    (a) 1(b) 2(c) 3(d) 4
  2. The perimeter of a square with side 10 cm is:
    (a) 20 cm(b) 30 cm(c) 40 cm(d) 100 cm
  3. A shape on a grid covers 6 rows of 3 squares each. Its area is:
    (a) 9 sq units(b) 15 sq units(c) 18 sq units(d) 36 sq units

E. Word Problems

  1. A farmer wants to put a fence around his rectangular field that is 45 m long and 30 m wide. What is the total length of fencing needed?
  2. Anita wants to put lace around a square handkerchief with side 22 cm. How much lace does she need?
  3. A shape drawn on a grid covers 4 rows with 7 squares in each row. What is its area in square units?
Fun Activity -- Shape Hunt at Home

Look around your house and find objects that match each 3D shape. Write the name of the object and the shape it looks like.

3D ShapeObject Found at Home
Cube
Cuboid
Sphere
Cylinder
Cone