Square Practice Questions

A square is a type of quadrilateral in which all four sides are equal and each interior angle measures 90°. It has two pairs of parallel sides, and its diagonals are equal in length and bisect each other at right angles.

Solved Examples

Example 1: A square has one of its sides measuring 24 cm. Calculate its area and perimeter.
Solution: 

Given,
Side of Square = 24 cm

Area of Square = a²
= 24 × 24 = 576 sq cm 

Perimeter of Square =  Sum of all sides of square = a + a + a + a = 4a 
P = 4 × 24 
P = 96 cm

Hence, area of square is 576 sq. cm and perimeter of square is 96 cm.

Example 2: Find the area of a square park whose perimeter is 420 ft.
Solution:   

Given,
Perimeter of Square Park = 420 ft
Perimeter of a Square = 4 × side
4 × side = 420
Side = 420/4
Side = 105 ft

Formulae for Area of a Square = side²
Hence, Area of Square Park = (105)² 
A = 105 × 105 = 11025 ft²

Thus, area of a square park whose perimeter is 420 ft is 11025 ft²

Practice Questions

Question 1: A square field has a perimeter of 400 m. Find its area.

Question 2: Calculate the area of a square swimming pool whose perimeter is 160 ft.

Question 3: A square park has a perimeter of 840 ft. Calculate its area.

Question 4: Find the area of a square courtyard whose perimeter is 200 ft.

Question 5: Find the area of a square playground whose perimeter is 440 ft.

Question 6: Find the area of a square playground whose perimeter is 180 ft.

Answer Key:

1. 100 m
2. 40 ft
3. 210 ft
4. 50 ft
5. 110 ft
6. 45 ft