Question

The adjacent sides of a parallelogram ABCD measures 34 cm and 20 cm, and the diagonal AC measures 42 cm. Find the area of the parallelogram.

Answer 1

In ||gm ABCD, AB= 34 cm, BC= 20 cm
and AC= 42 cm

$\because$ The diagonal of a parallelogram divides into two triangles equal in area,
Now area of $\Delta ABC,s=\frac{a+b+c}{2}=\frac{34+20+42}{2}=\frac{96}{2}=48\therefore Area=\sqrt{s(s-a)(s-b)(s-c)}=\sqrt{48(48-34)(48-20)(48-42)}=\sqrt{48\times 14\times 28\times 6}=\sqrt{4\times 4\times 3\times 2\times 7\times 7\times 2\times 2\times 2\times 3}=7\times 4\times 3\times 2\times 2=336c{m}^2$
$\therefore$ Area of ||gm ABCD = $2\times \text{area of triangle}=2\times 336=672c{m}^2$