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Area of square questions are provided here, along with detailed explanations to help students understand various techniques in solving word problems related to squares. In this article, you can practise various questions on finding the area of squares given with different parameters.
What is the Area of a square?
The area of a square is the amount of space occupied by a square shape in a two-dimensional plane. The formula to find the area of a square with side “a” is given by:
A = a2 = a × a
That means, Area of a square = (side)2
Also, the perimeter of a square = 4a
Learn more about the area of a square here.
1. Find the area of a square whose side is 11 units.
Solution:
Given,
Side of the square = 11 units
As we know, the area of a square = (side)2
= (11)2
= 11 × 11
= 121
Thus, the area of the square is 121 square units.
2. If the area of a square is 289 cm2, then find the measure of its side.
Solution:
Let a be the side of a square.
We know that the area of a square with side “a” = a2
So, a2 = 289 cm2 (given)
⇒ a = 17 cm
Hence, the measure of the side of the square is 17 cm.
3. Find the perimeter of a square whose area is 48 cm2.
Solution:
Let s be the side of a square.
Area of a square = s2
s2 = 48 cm2 (given)
⇒ s = √48 = 4√3
Thus, the side of a square = 4√3 cm
Perimeter of the square = 4s = 4(4√3) = 16√3 cm.
Area of a Square using its Diagonal
If “d” is the length of the diagonal of a square, then its area is equal to d2/2 square units.
i.e., Area of square = (½) × d2
Area of a Square using its Perimeter
Suppose P is the perimeter of a square then we can write the area of the square as:
Area of square = (P/4)2
4. What is the area of a square whose perimeter is given by 52 units?
Solution:
Given,
Perimeter of a square = P = 52 cm
As we know,
Area of a square = (P/4)2
= (52/4)2
= (13)2
= 169
Therefore, the area of the square is 169 square units.
5. Calculate the area of a square whose diagonal measures 15√2 cm.
Solution:
Given,
Diagonal of a square = d = 15√2 cm
We know that the area of a square with diagonal “d” = (½) × d2
= (½) × (15√2)2
= (½) × 15 × 15 × 2
= 225
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Hence, the area of the given square is 225 cm2.
6. If the ratio of diagonals of two squares is 5 : 2, then find the ratio of their corresponding areas.
Solution:
Given,
The ratio of the diagonals of two squares = 5 : 2
Let 5x and 2x be the diagonals of two squares, respectively.
Area of a square when diagonal is known = (1/2) × d2
Area of the first square = (1/2) × (5x)2
= (1/2) × (25x2)
= 25x2/2
Area of the second square = (1/2) × (2x)2
= (1/2) × (4x2)
= 2x2
Thus, the ratio of the areas of two squares = 2x2 : 25x2/2
= 4 : 25
7. The side of a square is 7 cm. If its side is doubled, how many times is the new square’s area bigger than the old square’s area?
Solution:
Given,
The side of a square = 7 cm
The area of the square = 7 × 7 = 49 cm2
Side of the new square = 2 × 7 = 14 cm
The area of the new square = 14 × 14 = 196 cm2
Here, 196 = 4 × 49
Hence, the area of the bigger square is four times the original square.
8. Find the cost of painting a square wall of side 13 m if the cost of painting is Rs. 30 per m².
Solution:
Given
Side of the square wall = 13 m
Area of the square wall = 13 m × 13 m = 169 m2
Also, given that the cost of painting one m2 = Rs. 30
Total cost of painting the wall = 169 × Rs. 30 = Rs. 5070
9. Calculate the area of a square lawn rounded by a path that is 2 m wide. Also, the area of the path is 160 m².
Solution:
Let x be the side length of a lawn.
So, the length of the lawn, including path = (x + 4) m
Given,
Area of the path = 160 m²
As we know,
Area of the path = Area of the lawn (including the path) – Area of the lawn
160 = (x + 4)² – x²
160 = x² + 8x + 16 – x²
160 = 8x + 16
144 = 8x
⇒ x = 144/8
⇒ x = 18
Hence, the area of the square lawn = 18² = 18 × 18 = 324 m²
10. What is the area of the square-shaped floor of the room, which is made up of 170 square tiles with a side of 30 cm?
Solution:
Side of a square tile = 30 cm
Area of the square tile = 30 × 30 = 900 cm2
Area of the floor with 170 tiles = 170 × 900 cm2 = 15300 cm2
Hence, the area of the square-shaped floor of the room is 15300 cm2.
Hi, @BrSmith, thanks for reaching out to let us know. It can be tricky when you are accepting payments for both business and personal use (such as a hobby)!
As a general rule, you want to always be processing payments with the Square Account that your goods/services are associated with.
For example, if you're providing professional services, you will need to be logged in and trading from your business account. If you are processing payments for a hobby, or personal use, you will need to be logged in and trading from your personal account.
What we advise in this instance, is that you sign up for a second Square Account that can serve as your personal account. For further assistance with this, please reach out to our Support Team directly and they will be able to provide more information about your recent payments.
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