Question

1. a square has a diagonal of length 5 cm. what is the area of the square? cm² (round to the nearest tenth)

Explanation:

Step1: Use the relationship between diagonal and side of square

Let the side of the square be \(a\). By Pythagorean theorem, \(a^{2}+a^{2}=d^{2}\) (where \(d\) is the diagonal). Given \(d = 5\), so \(2a^{2}=25\), then \(a^{2}=\frac{25}{2}\).

Step2: Calculate the area of the square

The area of a square \(A=a^{2}\). Since \(a^{2}=\frac{25}{2}=12.5\)

Answer:

\(12.5\)