NCERT Class 5 Mathematics | Chapter 3 | How Many Squares

CHAPTER – 3 | HOW MANY SQUARES?

In chapter 3, we learn about finding the area and perimeter of squares. Here are some points to remember:

• Total length of the boundary of a closed figure is perimeter.
• The surface covered by a closed figure is called its Area
• Area of a rectangle is length X breadth square units
• Area of square is side X side square units
• Perimeter of a rectangle is 2 X (length + breadth)
• Perimeter of a square is 4 X one side

Class 5 NCERT Chapter 3 Mathematics Practice Problems and Solutions

1. Write the area in square cm of the shaded portion?


Ans:

Total number of squares in the given figure = 16
The shaded portion is half of the given figure
So the area of the shaded portion = 8 square cm

2. Find the perimeter and area of the following figure

Ans:

Perimeter is the length of the boundary.
So perimeter = 18 cm
Area = Total number of squares = 20 square cm

3. Study the diagram given below. Draw 2 more lines so that the area is 18 square cm


Ans:

Consider the given square as four equal squares.
The first line is half of the first square.
So its area is 4.5 square cm
Area of the second square also 4.5 square cm
So total area is 9 square cm
So to get 18 square cm area we can draw two lines as follows:

4. Here is a rectangle of area 20 square cm.

a). Draw one straight line in this rectangle to divide it into two equal triangles. What is the area of each of the triangles?

Ans:

a)

Area of each triangle = ½ X area of rectangle
= ½ X 20 = 10 square cm
b) Draw one straight line in this rectangle to divide it into two equal rectangles. What is the area of each of the smaller rectangles?

Ans:

Area of each smaller rectangles = ½ area of bigger rectangle
= ½ X 20 = 10 square cm

c) Draw two straight lines in this rectangle to divide it into one rectangle and two equal triangles.

What is the area of the rectangle?
What is the area of each of the triangles?

Ans:

Area of rectangle = 10 square cm
Area of each triangle = ½ x area of smaller rectangle
= ½ X 10 = 5 square cm

5. Find the area and perimeter of a rectangle whose length is 8 cm and breadth is 2 cm?

Ans:

Area of a rectangle = length X breadth
= 8 X 2 = 16 square cm
Perimeter = 2 X (length + breadth)
= 2 X (8 + 2) = 2 X 10 = 20 cm

6. Find the perimeter of a square shaped flower bed of side 8 m?

Ans:

Perimeter of a square = 4 X side
= 4 x 8 = 32 m

7. Find the area of the following rectangles

a) length = 24 cm , breadth = 12 cm
b) length = 20 cm, breadth = 10 cm
c) Square of side 25 cm
d) square of side 40 cm

Ans:

a) Area = length X breadth
= 24 X 12 = 288 Square cm
b) Area = 20 X 10 = 200 Square cm
c) Area = Side X Side = 25 X 25 = 625 Square cm
d) Area = 40 X 40 = 1600 Square cm

8. A room is of length 5 m and breadth 4 m. Find the cost of cementing the room at the rate of Rs. 40 per square metre.

Ans:

Area of the room = length X breadth
= 5 X 4 = 20 square m
Cost of cementing the room = 20 X 40 =Rs. 800

9. Find the length of frame required for a portrait of length 500 cm and breadth 300 cm.

Ans:

Perimeter of frame = 2X (length + breadth)

= 2 X (500 + 300)
= 2 x 800
= 1600 cm

10. A rectangular garden of length 50 m and breadth 40 m needs to be fenced. Find the length of fencing required? What will be the cost of fencing at Rs . 40 per m.

Ans:

Perimeter of the garden = 2 x (l+b) = 2 X (50 + 40)
= 2x 90 = 180 m
Cost of fencing = 180 X 40 = Rs. 7200

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