Question

A rhombus and a square have the same base. If the diagonals of the rhombus measure 30 cm and 16 cm respectively, find the area of the square. 

(a) 225 cm² 

(b) 200 cm² 

(c) 240 cm² 

(d) 289 cm² 

Answer 1

(d) 289 cm²

Each side of the square = each side of the rhombus = \(\sqrt{\bigg(\frac{30}{2}\bigg)^2 + \bigg(\frac{16}{2}\bigg)^2}\)

= \(\sqrt{225+64}\) = \(\sqrt{289}\) = 17 cm

∴ Area of the square = (17)² cm² = 289 cm².