Question

A parallelogram has sides 60 m and 40m and one of its diagonals is 80 m long. Its area is

• A. $$500\sqrt{15}m^2$$
• B. $$600\sqrt{15}m^2$$
• C. $$400\sqrt{15}m^2$$
• D. $$450\sqrt{15}m^2$$

Answer 1

Answer:

$$600\sqrt{15}m^2$$

Semiperimeter of $\triangle{ABC},S=\frac{a+b+c}{2}$

$=\frac{60+40+80}{2}$

$s=90metre$

Area of $\triangle{ABC}=\sqrt{s(s-a)(s-b)(s-c)}$

$=\sqrt{90(90-60)(90-40)(90-80)}$

$=\sqrt{90\times{30}\times{50}\times{10}}$

$=\sqrt{3\times{30}\times{30}\times{5}\times{10}\times{10}}$

$=30\times{10}\sqrt{15}$

$=300\sqrt{15}sq.m$

Area of Paralellogram {ABCD}$=$2[Area of triangle ABC]

$=2\times{300}\sqrt{15}$

$=600\sqrt{15}sq.m$