Question

One side of a rhombus is 13 cm and one of its diagonals is 24 cm. What is the area (in cm²) of rhombus ?

• A. 30
• B. 90
• C. 120
• D. 60

Answer 1

Answer:

C. 120

Solution:

Given:

Side of rhombus = 13 cm

D1 (Diagonal) = 24 cm

Concept and Formula used:

Diagonals of a rhombus bisect each other at 90° 

Area of rhombus = 1/2 × (D1 × D2)

Where D1 and D2 are diagonals of the rhombus

Calculation:

Let the length of the other diagonal (D2) be 2x cm

As, diagonals of rhombus bisect each other at 90° 

AB = 24/2 = 12 cm

BC = 2x/2 = x cm

In ΔABC, ∠ABC = 90° 

AC2 = AB² + BC² 

⇒ 132 = 122 + x² 

⇒ 169 – 144 = x² 

⇒ x = 5 cm

D2 = 2x = 10 cm

Area of rhombus = 1/2 × (D1 × D2) = 1/2 × (10 × 24)

∴ Area of rhombus is 120 cm²