Question

What is the area of rhombus (in cm²) whose side is 10 cm and the shorter diagonal is 12 cm?

• A. 60
• B. 96
• C. 48
• D. 192

Answer 1

Answer:

B. 96

Solution:

Given:

The side of rhombus is 10 cm and its diagonal is 12 cm.

Formula Used:

1. Area of triangle $=\sqrt {s(s-a)(s-b)(s-c)}$

Where s = semi perimeter & a, b, and c are sides of the triangle

2. Area of rhombus (ABCD) = 2 × Area of Triangle 

Calculation:

Area of $\triangle{ABC}=\sqrt {s(s-a)(s-b)(s-c)}$

Semi perimeter of Δ ABC (s) $= \frac{(10 + 10 + 12)}{2}$

Semi perimeter of Δ ABC (s) = 16

Area of $\triangle{ABC}=\sqrt {16(16-10)(16-10)(16-12)}$

Area of $\triangle{ABC}=\sqrt {16 × 6 × 6 × 4}=48cm^2$

Area of rhombus (ABCD) = 2 × Area of Triangle = 96 cm²

∴ The area of rhombus is 96 cm².