Answer :
The area of the square is 112.5 units²
What is area of square?
The area of shape is the space enclosed within the perimeter or the boundary of a given shape.
A square is a quadrilateral with equal sides and angles. The area of a square is expressed as;
A = l²
where l is the length of the square.
using Pythagorean theorem to find L
15² = l² + l²
15² = 2l²
l² = 225/2
l² = 112.5 units²
Since the area of a square is given as l²
this means the area of the square is 112.5 units².
Therefore ;
A = 112.5 units²
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The area of the square shown with a diagonal of 15 is 112.5 unit²
What is an equation?
An equation is an expression that shows how numbers and variables are related to each other using mathematical operations.
Let x represent the length of each side of the square. To find the value of x, we use Pythagoras Theorem. Hence:
C² = x² + x²
Substituting:
15² = 2x²
2x² = 225
x² = 112.5
x = √112.5
The area of a square is the product of its sides. Hence:
Area = side * side
Area = (√112.5) * (√112.5)
Area = 112.5 unit²
The area of the square shown with a diagonal of 15 is 112.5 unit²
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