Calculating Areas and Perimeters of Squares
Area of a square: A = s^2, where s is the length of one of its sides
Perimeter of a square: P = 4s, where s is the length of one of its sides
Question 1:
A square has a perimeter of 28cm. What is its area?
Solution:
P = 4s
28 = 4s
s = 7cm
__A = s^2
A = 7^2
A = 49cm^2
Requested by: Anonymous
Question 2:
Find the perimeter of a square with a side length of 5cm.
Solution:
P = 4s
P = 4(5)
P = 20cm
Requested by: Anonymous
Question 3:
Find the area of a square with a side length of 8cm.
Solution:
A = s^2
A = 8^2
A = 64cm^2
Requested by: Arslan
Question 4:
Find the area and perimeter of a square with a side length of 6 cm.
Solution:
Area = s^2 = 6 cm * 6 cm = 36 cm^2
Perimeter = 4s = 4 * 6 cm = 24 cm
Requested by: Ritaaj
Question 5:
Find the area of a square with perimeter 32 cm.
Solution:
Perimeter = 4s, where s is the side length of the square.
32 cm = 4s
s = 8 cm
Therefore, the area of the square is:
Area = s^2 = 8 cm * 8 cm = 64 cm^2
Requested by: Ritaaj
Question 6:
Find the area and perimeter of a square with a diagonal length of 10 cm.
Solution:
To find the side length of the square, we can use the Pythagorean theorem:
a^2 + b^2 = c^2, where a and b are the length of the two sides and c is the length of the hypotenuse (the diagonal of the square).
In a square, a = b, so we have:
2a^2 = c^2
a^2 = (1/2)c^2
a = (1/2)c (since a must be positive and smaller than c)
Therefore, the side length of the square is:
s = a = (1/2)c = (1/2) * 10 cm = 5 cm
Area = s^2 = 5 cm * 5 cm = 25 cm^2
Perimeter = 4s = 4 * 5 cm = 20 cm
Requested by: Ritaaj
Question 7:
A square has a perimeter of 28cm. What is the length of each side?
Solution:
Perimeter of a square = 4s,
where s is the length of each side.
Given, perimeter = 28cm
28 = 4s
s = 7cm
Requested by: Mustakeem
Question 8:
A square has a diagonal of 6√2 cm. What is the area of the square?
Solution:
Area of a square = s^2, where s is the length of each side.
The diagonal of a square is the hypotenuse of a right-angled triangle with sides s and s.
Given, diagonal = 6√2 cm
By Pythagoras theorem, (s^2 + s^2) = (6√2)^2
2s^2 = 72
s^2 = 36
Area = s^2 = 36cm^2
Requested by: Mustakeem
Question 9:
A square has an area of 121m^2. What is the length of each side?
Solution:
Area of a square = s^2, where s is the length of each side.
Given, area = 121m^2
s^2 = 121
s = 11m
Requested by: Faisal
Question 10:
A square has a perimeter of 40mm. What is the area of the square?
Solution:
Perimeter of a square = 4s, where s is the length of each side.
Given, perimeter = 40mm
40 = 4s
s = 10mm
Area = s^2 = 100mm^2
Requested by: Faisal
Question 11:
Find the perimeter of a square with side length 6cm.
Solution:
P = 4s
P = 4(6)
P = 24cm
Requested by: Anonymous
Question 12:
Find the area of a square with side length 8cm.
Solution:
A = s^2
A = 8^2
A = 64cm^2
Requested by: Khalid
Question 13:
A square has a perimeter of 36m. What is the length of each side?
Solution:
P = 4s
36 = 4s
s = 9m
Requested by: Khalid
Question 14:
A square has an area of 49cm^2. What is the length of each side?
Solution:
A = s^2
49 = s^2
s = 7cm
Requested by: Khalid
Question 15:
Find the perimeter of a square with diagonal length 10cm.
Solution:
Let s be the side length of the square.
By Pythagoras theorem: s^2 + s^2 = 10^2
2s^2 = 100
s^2 = 50
s = √50 cm
P = 4s
P = 4(√50)
P = 4(5√2) cm
Requested by: Khalid
Question 16:
A square has an area of 169cm^2. Find the length of its side.
Solution:
A = s^2
169 = s^2
s = √169
s = 13cm
Requested by: Mansoor
Question 17:
A square has a perimeter of 64cm. Find the length of its side.
Solution:
P = 4s
64 = 4s
s = 16cm
Requested by: Mansoor
Question 18:
Find the perimeter of a square with an area of 49cm^2.
Solution:
A = s^2
49 = s^2
s = 7cm
P = 4s
P = 4(7)
P = 28cm
Requested by: Mansoor
Question 19:
A square has a perimeter of 40cm. Find its area.
Solution:
P = 4s
40 = 4s
s = 10cm
A = s^2
A = 10^2
A = 100cm^2
Requested by: Mansoor
Question 20:
Find the perimeter of a square with a diagonal of 10cm.
Solution:
P = 4s
d = √2s
10 = √2s
s = 10/√2
P = 4(10/√2)
P ≈ 28.28cm
Requested by: Haroon
Question 21:
Find the area of a square with a diagonal of 12cm.
Solution:
d = √2s
12 = √2s
s = 12/√2
A = s^2
A = (12/√2)^2
A ≈ 144cm^2
Requested by: Haroon
Question 22:
Find the perimeter of a square with an area of 81cm^2.
Solution:
A = s^2
81 = s^2
s = 9cm
P = 4s
P = 4(9)
P = 36cm
Requested by: Haroon
Question 23:
A square has a diagonal of 10cm. Find its area.
Solution:
d = √2s
10 = √2s
s = 10/√2
A = s^2
A = (10/√2)^2
A ≈ 50cm^2
Requested by: Haroon
Question 24:
Find the perimeter of a square with a side length of 3.5cm.
Solution:
P = 4s
P = 4(3.5)
P = 14cm
Requested by: Bilal
Question 25:
Find the area of a square with a perimeter of 20cm.
Solution:
P = 4s
20 = 4s
s = 5cm
A = s^2
A = 5^2
A = 25cm^2
Requested by: Bilal
Question 26:
A square has an area of 25cm^2. Find its perimeter.
Solution:
A = s^2
25 = s^2
s = 5cm
P = 4s
P = 4(5)
P = 20cm
Requested by: Bilal
Question 27:
A square has a diagonal of 8cm. Find its perimeter.
Solution:
d = √2s
8 = √2s
s = 8/√2
P = 4s
P = 4(8/√2)
P ≈ 22.63cm
Requested by: Bilal
