Question

The perimeter of a rhombus is 48 cm and the measure of an angle is 60°, then the area of rhombus is?
1. 48√3 cm²
2. 72√3 cm2
3. 86√2 cm2
4. 32√2 cm2

Answer 1

Correct Answer - Option 2 : 72√3 cm2

Given:

The perimeter of a rhombus is 48 cm.

The measure of an angle is 60°

Formula Used:

Area of rhombus = a²× sinθ,

Perimeter of rhombus = 4a, a is the side of a rhombus

Calculation:

Perimeter of rhombus = 4a

⇒ 48 = 4 × a

⇒ a = 48/4

⇒ a = 12 cm

Area of rhombus = a2 × sinθ

⇒ Area of rhombus = 12² × sin60° 

We know that sin60° = √3/2

⇒ Area of rhombus = 144 × √3/2

⇒ Area of rhombus = 72√3

∴ Area of rhombus is 72√3 cm²