Question

The adjacent sides of a parallelogram ABCD are AB = 34cm, BC = 20cm and diagonal AC = 42cm. Find the area of the parallelogram.

• A. $670c{m}^2$
• B. $672c{m}^2$
• C. $595c{m}^2$
• D. $550c{m}^2$

Answer 1

The correct option is B

$672c{m}^2$

In $\Delta ABC$, it is given that

a = BC = 20cm, b = AC = 42cm and c = AB = 34cm

$\therefore s=\frac{1}{2}(20+42+34)cm=48cm$

$\therefore (s-a)=28cm,(s-b)=6cm$ and $(s-c)=14cm$.

$\therefore$ area of $\Delta ABC=\sqrt{s(s-a)(s-b)(s-c)}$

$=\sqrt{48\times 28\times 6\times 14}c{m}^2=(14\times 24)c{m}^2$

$=336c{m}^2$

$\therefore$ area of parallelogram

ABCD $=2\times \left(areaof\Delta ABC\right)$

$=(2\times 336)c{m}^2=672c{m}^2$