Question

In a parallelogram ABCD, the diagonal AC measures 34 m and the perpendicular distance of AC from either of the vertices B or D is 12 m. Find the area of the parallelogram.

• A. 204 sq. m
• B. 408 sq. m
• C. 816 sq. m
• D. 806 sq. m

Answer 1

The correct option is B 408 sq. m


In $\Delta ABC$,
base $=AC=34m$
height $=BM=12m$
Area of $\Delta ABC=\frac{1}{2}\times 34\times 12$$=204m^2$
Similarly, the area of $\Delta ADC=204m^2$
Area of parallelogram = Area of $\Delta ABC$ + Area of $\Delta ADC$
$=(204+204)m^2=408m^2$
$\Rightarrow$ The area of the parallelogram is 408 m${}^2$.