Area of Squares and Rectangles: Questions and Solutions

Area of Squares and Rectangles Questions with solutions presents methods and worked examples for calculating the area of two fundamental plane figures. This guide reviews the standard formulas: area of a rectangle = length × breadth and area of a square  = side² and demonstrates their use through solved examples. From basic calculations to problems involving unit conversion and composite figures, each solution focuses on clear steps, logical reasoning, and useful shortcuts. Worked examples with brief explanations help strengthen understanding and exam preparation.

Table of Contents

• Area of Square and Rectangle: Formulas at a Glance
• Solved Examples: Area of Square and Rectangle Questions
• Practice Questions on Area of Square and Rectangle
• Frequently Asked Questions of Area of Squares and Rectangles Questions

Area of Square and Rectangle: Formulas at a Glance

The area of a square is found by multiplying its side by itself, and the area of a rectangle is found by multiplying its length by its breadth. Both answers are always expressed in square units.

For a Square

 

For a Rectangle

 

Solved Examples: Area of Square and Rectangle Questions

Q1. Meera's chart paper is a perfect square with each side measuring 14 cm. Find its area.

Solution:

Side of the square = 14 cm

Area = side × side = 14 × 14 = 196 cm²

Answer: 196 cm²

Q2. Arjun's vegetable garden is rectangular in shape, measuring 25 m in length and 18 m in breadth. Find the area of the garden.

Solution:

Length = 25 m, Breadth = 18 m

Area = length × breadth = 25 × 18 = 450 m²

Answer: 450 m²

Q3. Priya has a square dupatta whose area is 225 cm². Find the length of each side.

Solution:

Area = side²

225 = side²

side = √225 = 15 cm

Answer: The side of the dupatta is 15 cm.

Q4. The area of a rectangular notice board is 288 cm², and its length is twice its breadth. Find its length and breadth.

Solution:

Let breadth = b, so length = 2b

Area = length × breadth

288 = 2b × b = 2b²

b² = 144

b = 12 cm, so length = 2 × 12 = 24 cm

Answer: Length = 24 cm, Breadth = 12 cm

Q5. The perimeter of a square park where children play cricket every evening is 96 m. Find the area of the park.

Solution: 

Perimeter = 4 × side = 96 m

side = 96 ÷ 4 = 24 m

Area = 24 × 24 = 576 m²

Answer: 576 m²

Q6. A rectangular field used for the school's Annual Day has a perimeter of 154 m. If its length is 47 m, find its breadth and area.

Solution:

Perimeter = 2 × (length + breadth) = 154 m

length + breadth = 77 m

breadth = 77 − 47 = 30 m

Area = 47 × 30 = 1410 m²

Answer: Breadth = 30 m, Area = 1410 m²

Q7. The diagonal of a square study table top measures 10√2 cm. Find its area.

Solution:

Area = d² / 2

= (10√2)² / 2

= (100 × 2) / 2

= 200 / 2 = 100 cm²

Answer: 100 cm²

Q8. A rectangular television screen has a diagonal of 25 inches and a width of 15 inches. Find the area of the screen.

Solution:

Using Pythagoras theorem: length² + width² = diagonal²

length² = 25² − 15² = 625 − 225 = 400

length = √400 = 20 inches

Area = length × width = 20 × 15 = 300 sq. inches

Answer: 300 square inches

Q9. Rohit's father wants to paint a square wall of his terrace room that measures 6 m on each side. If the painter charges ₹45 per square metre, find the total cost.

Solution:

Area of the wall = 6 × 6 = 36 m²

Cost of painting = 36 × ₹45 = ₹1,620

Answer: ₹1,620

Q10. A rectangular hall in Ananya's housing society measures 12 m by 9 m. If flooring costs ₹350 per square metre, find the total cost of flooring the hall.

Solution: 

Area of hall = 12 × 9 = 108 m²

Cost = 108 × ₹350 = ₹37,800

Answer: ₹37,800

Q11. A rectangular garden measuring 40 m by 30 m has a uniform path 2.5 m wide built all around it, outside its boundary. Find the area of the path.

Solution: 

Since the path runs around all four sides, it adds 2.5 m on every side.

Outer length = 40 + 2.5 + 2.5 = 45 m

Outer breadth = 30 + 2.5 + 2.5 = 35 m

Area of garden + path = 45 × 35 = 1575 m²

Area of garden alone = 40 × 30 = 1200 m²

Area of path = 1575 − 1200 = 375 m²

Answer: 375 m²

Q12. The floor of a square community hall with a side of 9 m needs to be covered with square tiles of side 30 cm. How many tiles are needed?

Solution:

First, convert to the same unit. 9 m = 900 cm

Area of the hall = 900 × 900 = 8,10,000 cm²

Area of one tile = 30 × 30 = 900 cm²

Number of tiles = 8,10,000 ÷ 900 = 900 tiles

Answer: 900 tiles

Q13. A study room is L-shaped: a rectangular section measuring 8 m by 5 m, with a square reading nook of side 3 m attached to it. Find the total floor area of the room.

Solution:

Area of rectangular section = 8 × 5 = 40 m²

Area of square nook = 3 × 3 = 9 m²

Total area = 40 + 9 = 49 m²

Answer: 49 m²

Q14. If the side of a square is doubled, and separately, if both the length and breadth of a rectangle are doubled, how does the area change in each case?

Solution:

Square: Let original side = a, so original area = a².

New side = 2a, new area = (2a)² = 4a².

The area becomes 4 times the original.

Rectangle: Let original length = l, breadth = b, so original area = l × b.

New length = 2l, new breadth = 2b, new area = 2l × 2b = 4lb.

The area also becomes 4 times the original.

Answer: In both cases, doubling every dimension makes the area 4 times larger.

Q15. The sides of two square flower beds are in the ratio 3:5. Find the ratio of their areas.

Solution:

Let the sides be 3x and 5x.

Area of first square = (3x)² = 9x²

Area of second square = (5x)² = 25x²

Ratio of areas = 9x² : 25x² = 9 : 25

Answer: 9 : 25

Practice Questions on Area of Square and Rectangle

1. True or False

A square can be considered a special type of rectangle.

2. Two rectangular photo frames are similar in shape, with their corresponding sides in the ratio 2:3. Find the ratio of their areas.

3. Assertion (A): The area of a square with side 8 cm is 64 cm².

Reason (R): The area of a square is always equal to twice its side.

Choose: (a) Both A and R are true, and R explains A   

(b) Both A and R are true, but R does not explain A   

(c) A is true, R is false   

(d) A is false, R is true

14. A square garden and a rectangular garden have the same perimeter of 80 m. The rectangle's length is 25 m. Which garden has a larger area?

(a) The square

(b) The rectangle

(c) Both are equal

(d) Cannot be determined

5. Fill in the Blank

If the area of a rectangle is A and its length is l, then its breadth = ______.

6. A square-shaped kitchen floor of side 4 m is to be tiled with rectangular tiles measuring 40 cm by 25 cm. Find the number of tiles required.

7. True or False

Two rectangles with the same area must always have the same perimeter.

8. The diagonal of a rectangle is 13 cm and its breadth is 5 cm. What is its area?

(a) 48 cm²

(b) 60 cm²

(c) 65 cm²

(d) 120 cm²