Question

Perimeter of the rhombus is $100m$ and its diagonal is $40m$. Find the area of rhombus.

• A. $625m^2$
• B. $1000m^2$
• C. $400m^2$
• D. $600m^2$

Answer 1

The correct option is D $600m^2$

Perimeter of rhombus $=4\times side$

$\Rightarrow$ $100=4\times side$

$\Rightarrow$ $side=\frac{100}{4}$

$\Rightarrow$ $side=25$

We know diagonals of a rhombus divides the rhombus in two equilateral triangle.

Now, we are going to find area of $1$ equilateral triangle.

Semi perimeter $=\frac{25+25+40}{2}=45$

We will use Heron's formula to find are of equilateral triangle.

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

$=\sqrt{45(45-40)(45-25)(45-25)}$

$=\sqrt{45\times 5\times 20\times 20}$

$=\sqrt{90000}$

$=300m^2$

$\Rightarrow$ Area of rhombus $=2\times 300m^2=600m^2$