Question

The perimeter of a rhombus is 68 cm and one of its diagonals is 16 cm. Find the area of the rhombus.

Options

• 240 sq cm

• 220 sq cm

• 200 sq cm

• 320 sq cm

Answer 1

240 sq cm

Explanation:

Let the diagonal be ‘d’

Perimeter be ‘P’

We know, Perimeter = 4 × side

⇒ 68 = 4 × side

⇒ side = `68/4` = 17 cm

As one diagonal = 16 cm

We know, all side are equal.

∴ Other diagonal = `2sqrt({17^2 - (16/2)^2})`

= `2sqrt(17^2 - 8^2)`

= 2 × 15

= 30 cm

∴ Area = `"Product of diagonals"/2 = (16 xx 30)/2` = 240 cm²