Question

The side of a rhombus is 10 cm and one diagonal is 16 cm. The area of the rhombus is 

(a) 96 cm² 

(b) 95 cm² 

(c) 94 cm² 

(d) 93 cm² 

Answer 1

(a) 96 cm²

Since the diagonals of a rhombus bisect each other at right angles. 

In Δ AOB, BO² = \(\sqrt{AB^2-AO^2}\)

= \(\sqrt{100-64}\) cm

= \(\sqrt{36}\) = 6 cm 

∴ The other diagonal = 2 × 6 cm = 12 cm 

∴ Area of the rhombus = \(\frac12\) × 16 cm × 12 cm = 96 cm².