Question

The length of a diagonal of a square is 7.5 mm. Find the area of the square.

Answer 1

By Pythagoreans' theorem,

7.5² = l² × b²
56.25 = l² × b²

Since l = b
56.25 ÷ 2
= l²/b²
= 28.125 mm

∴ l = √28.125
= 5.3033 mm

Area of square
= √28.125 × √28.125
= 28.125 mm²
≈ 28.1 mm² (3s.f.)