Question

A field in the form of parallelogram has sides 60m and 40m and one of its diagonals is 80m long. Find the area of parallelogram.

• A. $620\sqrt{15}{m}^2$
• B. $580\sqrt{15}{m}^2$
• C. $610\sqrt{15}{m}^2$
• D. $600\sqrt{15}{m}^2$

Answer 1

The correct option is D $600\sqrt{15}{m}^2$

$s=\frac{AB+BC+AC}{2}=\frac{180}{2}=90m$
$Area\left(\Delta ABC\right)$
$=s\sqrt{s(s-AB)(s-BC)(s-AC)}$
$=\sqrt{90(90-60)(90-40)(90-80)}$
$=\sqrt{90\times 30\times 50\times 10}$
$=\sqrt{1350000}$
$=\sqrt{15\times 90000}$
$=300\sqrt{15}{m}^2$
$\therefore Area\left(\Delta ABCD\right)$
$=2\times 300\sqrt{15}=600\sqrt{15}{m}^2$