Question

The area of a parallelogram whose diagonal is 6.8 cm and the perpendicular distance of this diagonal from an opposite vertex is 7.5 cm is

• A. 25.5 $c{m}^2$
• B. 11.9 $c{m}^2$
• C. 12.5 $c{m}^2$
• D. 51 $c{m}^2$

Answer 1

The correct option is D 51 $c{m}^2$

We know that a diagonal divides a parallelogram into two congruent triangle and area of congruent triangle are equal.
So, for one of the triangles, if the diagonal is the base, then the perpendicular distance is the height.
Area of each triangle $=\frac{1}{2}\times$ base $\times$ height $=\frac{1}{2}\times 6.8\times 7.5=25.5sqcm$
So, area of the parallelogram $=2\times 25.5=51sqcm$