Question

The side of a rhombus is 10 cm and one of its diagonals is 16 cm. Find its area.

• A. $90c{m}^2$
• B. $96c{m}^2$
• C. $85c{m}^2$
• D. $100c{m}^2$

Answer 1

The correct option is

A

$96c{m}^2$

Area of rhombus $=2\times \text{area of}\Delta ABC$

Area of one triangle whose sides are 10cm, 10cm, 16 cm is given by -

S =$\frac{10+10+16}{2}=18cm$

Now, area of triangle = $\sqrt{18(18-10)(18-10)(18-16)}$
= $\sqrt{18\left(8\right)\left(8\right)\left(2\right)}$
= $\sqrt{\left(9\right)\left(2\right)\left(8\right)\left(8\right)\left(2\right)}$
=$8\times 2\times 3=48$

Hence, area of rhombus $=2\times 48=96c{m}^2$