Question

one of the angles of a rhombus is 120 and its sides are15cmlong.Find the area of the rhombus

Answer 1

Answer:

Step-by-step explanation:

Consider the rhombus as shown in the above diagram, where ∠BAD = 120° and each side is 15 cm long.

The diagonal of a rhombus bisects the interior angle.

∠MAD = 120°/2 = 60°

In rt-ΔAND:

AM = 15 cos(60°) cm = 15/2 cm

MD = 15 sin(60°) cm = (15√3)/2 cm

The diagonals of a rhombus bisects and is perpendicular to each other.

AC = (15/2) × 2 cm = 15 cm

BD = [(15√3)/2] × 2 cm = 15√3 cm

Area of the rhombus

= (1/2) × AC × BD

= (1/2) × 15 × (15√3) cm²

= (225√3)/2 cm²

≈ 194.86 cm²