Question

Find the area of a rhombus with side 4 cm and one of its angles is 120°.

Answer 1

Given: Side of rhombus a = 4 cm and one of its angles θ = 120°.

Stepwise calculation:

1. The area of a rhombus is given by the formula:

Area = a² sin θ

2. Substitute values:

Area = 4² × sin 120°

= 16 × sin 120°

3. Use sin 120° = sin(180° – 60°)

= sin 60°

= `sqrt(3)/2 ≈ 0.866` 

4. Calculate the area:

Area = 16 × 0.866

Area = 13.856 cm²

The area of the rhombus with side 4 cm and an angle of 120° is approximately 13.856 cm².