Question

Find the area of a parallelogram $ABCD$ in which $AB=3cm,BC=7cm$ and $AC=8cm$ using Heron's formula.

• A. 6 cm²
• B. 12 cm²
• C. 18 cm²
• D. 24 cm²

Answer 1

The correct option is B

12 cm²

Since, $ABCD$ is a parallelogram, its opposite sides will be equal.
$\Rightarrow CD=AB=3cm$ and $AD=BC=7cm$

Now in triangle ABC,

Calculating area of the triangle using heron’s formula,

$s=\frac{\text{Perimeter}}{2}=\frac{AB+BC+AC}{2}=\frac{3+7+8}{2}=9cm$
$\Rightarrow$ Area $=\sqrt{s(s-a)(s-b)(s-c)}$
$=\sqrt{9(9-3)(9-7)(9-8)}$
$=\sqrt{9\times 6\times 2\times 1}$
$=6\sqrt{3}c{m}^2$
Now, area of the parallelogram $=2\times$ Area of triangle $ABC$

$\Rightarrow$ The area of the parallelogram $=2\times 6\sqrt{3}=12\sqrt{3}c{m}^2$