Question

The perimeter of a rhombus is 100 cm and one of the diagonals is 48 cm The area of the rhombus in sq cm is :
1. 84
2. 168
3. 336
4. 175

Answer 1

Correct Answer - Option 3 : 336

Given:

Perimeter of rhombus is 100cm

One diagonal is 48cm

Formula:

Area of rhombus = 1/2 × product of diagonals

Calculations:

Side of a rhombus,

⇒ 100/4 = 25cm

Diagonals of a rhombus bisect each other,

Half of one diagonal,

⇒48/2 = 24cm

Using Pythagoras theorem,

side² = (half of one diagonal)² + (half of other diagonal)²

Half of other diagonal,

⇒ √625 - 576 = 7 cm

Length of other diagonal,

⇒ 7 × 2 = 14cm

∴ Area of rhombus = 1/2 × 48 × 14 = 336 cm²