Question

A parallelogram has sides $30m,70m$ and one of its diagonals is $80m$ long. Its area will be

• A. $600m^2$
• B. $1200\sqrt{3}{m}^2$
• C. $1200m^2$
• D. $600\sqrt{3}{m}^2$

Answer 1

Answer: (B)

$1200\sqrt{3}{m}^2$

The diagonal of parallelogram divides it into two congruent triangles.

$\therefore$ Area (parallelogram $ABCD)=2\times$ Area $\left(\Delta ABC\right)$

In $\Delta ABC$,

$s=\frac{80m+30m+70m}{2}=\frac{180m}{2}=90m$

$\therefore Area=\sqrt{90(90-80)(90-30)(90-70)}{m}^2$

$=\sqrt{90\times 10\times 60\times 20m^2}$

$=600\sqrt{3}{m}^2$

$\therefore$ Area of parallelogram $ABCD=$$2\times 600\sqrt{3}{m}^2$ $=1200\sqrt{3}{m}^2$