Question

The side of a rhombus is $10cm$ and one diagonal is $16cm.$ The area of the rhombus is

• A. $96{\text{cm}}^2$
• B. $48{\text{cm}}^2$
• C. $24{\text{cm}}^2$
• D. Data Insufficient to calculate area

Answer 1

Answer: (A)

$96c{m}^2$

Given: Sides of rhombus $=10cm$

One Diagonal $=16cm$

For triangle ABC, we have

three sides are: $a=AB=10cm,b=BC=10cm,c=AC=16cm$
Semi-perimeter, $s=\frac{a+b+c}{2}=\frac{10+10+16}{2}=\frac{36}{2}=18$

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

$=\sqrt{18(18-10)(18-10)(18-16)}$

$=\sqrt{18\left(8\right)\left(8\right)\left(2\right)}$

$=\sqrt{2304}$

$=48c{m}^2$
Area of the rhombus ABCD $=2\times$(Area of the triangle ABC)

[$\because$ Sides of both triangle ABC and triangle ADC are same]
$=2\left(48\right)=96c{m}^2$