Question

One side of a rhombus is 20 cm long and one of its diagonals measures 24 cm. The area of the rhombus is ______.

Options

• 192 cm²

• 480 cm²

• 240 cm²

• 384 cm²

Answer 1

One side of a rhombus is 20 cm long and one of its diagonals measures 24 cm. The area of the rhombus is 384 cm².

Explanation:

Let ABCD be the rhombus in which AB = 20 cm and `OA = (1/2 xx 24) cm = 12  cm`.

∴ OB² = AB² – OA²

= [(20)² – (12)²] cm²

= 256 cm² = (16)² cm²

⇒ OB = 16 cm.

∴ BD = (2 × 16) cm

= 32 cm

∴ Area = `(1/2 xx 24 xx 32) cm^2`

= 384 cm²