Question

The length of a diagonal of a parallelogram is 70 cm and lengths of perpendiculars on this diagonal from its opposite vertices are 27 cm each. The area of the parallelogram is
(a) 1800 cm²
(b) 1836 cm²
(c) 1890 cm²
(d) 1980 cm²

Answer 1

(c) 1890 cm²

A diagonal of a parallelogram divides it into two congruent triangles, as shown in the figure.


Here, the area of the parallelogram is twice the area of each triangle.

Thus, we have:

$$\begin{gathered} \mathrm{Area}\mathrm{of}\mathrm{parallelogram}=2\left(\mathrm{Area}\mathrm{of}\mathrm{each}\mathrm{triangle}\right) \\ =2\left(\frac{1}{2}\times \mathrm{Base}\times \mathrm{Height}\right) \\ =2\left(\frac{1}{2}\times 70\times 27\right) \\ =1890{\mathrm{cm}}^2 \end{gathered}$$