Question

A parallelogram has sides 15 cm and 7 cm long. The length of one of the diagonals is 20 cm. The area of the parallelogram is

• A. 144 sq.cm
• B. 225 sq.cm
• C. 336 sq.cm
• D. 84 sq.cm

Answer 1

Answer:

D. 84 sq.cm

Area of parallelogram ABCD = Area of 2 $\triangle{ABC}$

Semi-perimeter of $\triangle{ABC}$

$S=\frac{20+7+15}{2}=\frac{42}{2}=21cm$

Area of $\triangle{ABC}$

$=\sqrt{s(s-a)(s-b)(s-c)}$

$=\sqrt{21(21-7)(21-15)(21-20)}$

$=\sqrt{21\times{14}\times{6}\times{1}}$

$=42cm^2$

Area of parallelogram = 2 × 42 = 84 sq. cm.