Answer :

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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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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