Q25. - Geometry

Question

Find the area of a square with diagonals of length  d

Step-by-Step Solution

Answer

The area of the square is  $\left(A\right)=\frac{d^2}{2}$

Step 1. Given information.

Length of the diagonal is d

Step 2. Concept Used.

 The length of the diagonal is d

Then,   the area of the square when the diagonal is given.

$A=\frac{1}{2}{\left(diagonal\right)}^2$

Step 3. Let’s calculate the area of square.

Put the value of diagonal  into the formula and find the area.

Area of the square :

$\begin{array}{l}A=\frac{1}{2}{\left(diagonal\right)}^2\\ A=\frac{1}{2}{\left(d\right)}^2\\ A=\frac{d^2}{2}\end{array}$

Therefore, the area of the square is $\frac{d^2}{2}.$