Question

a square has a diagonal of length 5 cm. what is the area of the square? type your answer in the box. \boxed{} cm²

Explanation:

Step1: Recall square diagonal - side relation

For a square with side \( s \) and diagonal \( d \), the Pythagorean theorem gives \( d^{2}=s^{2} + s^{2}=2s^{2} \).

Step2: Find side squared (related to area)

The area of a square is \( A = s^{2} \). From \( d^{2}=2s^{2} \), we can solve for \( s^{2} \): \( s^{2}=\frac{d^{2}}{2} \). Given \( d = 5\space\text{cm} \), then \( s^{2}=\frac{5^{2}}{2}=\frac{25}{2}=12.5 \). Since \( A=s^{2} \), the area is \( 12.5\space\text{cm}^2 \).

Answer:

\( 12.5 \)