Question

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

• A. 672 $c{m}^2$
• B. 772 $c{m}^2$
• C. 336 $c{m}^2$
• D. 1008 $c{m}^2$

Answer 1

The correct option is A 672 $c{m}^2$

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

Consider △ABC.
$s=\frac{a+b+c}{2}=\frac{34+20+42}{2}=\frac{96}{2}=48\therefore Area=\sqrt{s(s-a)(s-b)(s-c)}=\sqrt{48(48-34)(48-20)(48-42)}=\sqrt{48\times 14\times 28\times 6}=7\times 4\times 3\times 2\times 2=336c{m}^2$

The diagonal of a parallelogram divides it into two triangles of equal area.
$\therefore$ Area of ||gm ABCD = $2\times \text{area of triangle ABC}=2\times 336c{m}^2=672c{m}^2$