Each side of a rhombus is 15 cm and the length of one of its diagonals is 24 cm. The area of the rhombus is

Question

Philoid · Accepted Answer

Given: A rhombus ABCD

Diagonal AC = 24 cm

Side length : AB = BC = CD = DA = 15 cm

We know that diagonals of the rhombus bisect each other right angles.

AO = AC

⇒AO = ( × 24) cm

⇒AO = 12 cm

From right AOB, we have :

BO² = AB² – AO²

⇒BO² = AB² – AO²

⇒BO² = 15² – 12²

⇒BO² = 225 – 144

⇒BO² = 81

⇒BO = 9 cm

BD = 2 × BO

BD = 2 × 9 = 18 cm

Hence, the length of the other diagonal is 18 cm.

Area of the rhombus = × 24 × 18 = 216 cm²