Question

The two adjacent sides of a parallelogram are $5$ cm and $4$ cm respectively and if the respective diagonal is $7$ cm, then find the area of the parallelogram?

• A. $8\sqrt{6}$
• B. $6\sqrt{6}$
• C. $4\sqrt{6}$
• D. $8\sqrt{3}$

Answer 1

The correct option is A $8\sqrt{6}$

Here, $ABCD$ is a parallelogram,

$AB=5cm,BC=4cm$ and $AC=7cm$

$ar\left(△ABC\right)=\sqrt{S(S-a)(S-b)(S-c)}$

$S=\frac{5+4+7}{2}=\frac{16}{2}=8$

Now,

$ar\left(△ABC\right)=\sqrt{8(8-5)(8-4)(8-7)}$

$=\sqrt{8\times 3\times 4\times 1}$

$=\sqrt{96}$

$=4\sqrt{6}c{m}^2$

Area of parallelogram $ABCD=2\times ar\left(△ABC\right)$

$=2\times 4\sqrt{6}$

$=8\sqrt{6}c{m}^2$