SSC CPO 2023 PYQ — Question 148

The correct answer is option 3 i.e. 240 cm²

Given:

ABCD is a rhombus

AB = BC = CD = DA = 17 cm

AC = 16 cm

Formula used:

Area of rhombus = (1/2) × d1 × d2

Where d1 and d2 are the diagonals of the rhombus

Calculations:

Therefore, AO = 8 cm (Diagonals of a rhombus bisect each other at 90)

In ∆AOD,

AD² = AO² + OD²

⇒ 17² = 8² + OD²

⇒ 289 = 64 + OD²

⇒ 225 = OD²

⇒ OD = 15 cm

Therefore, BD = 2 × OD = 2 × 15 = 30 cm

Hence, area of rhombus = 1/2 × 16 × 30 = 240 cm²