Question

In a parallelogram $ABCD,AB=16cm,BC=12cm$ and diagonal $AC=20cm$. Find the area of the parallelogram.

Answer 1

In $△ABC$,

$s=\frac{AB+BC+CA}{2}$

$\Rightarrow s=\frac{12+20+16}{2}=24cm$

By using Heron's formula,$\Rightarrow A=\sqrt{s(s-a)(s-b)(s-c)}$

Area of $△ABC\left(A\right)=\sqrt{24(24-16)(24-12)(24-20)}$

$\Rightarrow A=\sqrt{24\times 8\times 12\times 4}=96{cm}^2$

Therefore,

As we know that the diagonal of a parallelogram divides it into two equal triangles.

Therefore,

Area of parallelogram $=2A=2\times 96=192{cm}^2$