**Question:**

*Mark (✓) against the correct answer:*

The diagonal of a quadrilateral is 20 cm in length and the lengths of perpendiculars on it from the opposite vertices are 8.5 cm and 11.5 cm. The area of the quadrilateral is

(a) 400 cm2

(b) 200 cm2

(c) 300 cm2

(d) 240 cm2

**Solution:**

(b) 200 cm2

Let $A B C D$ be a quadilateral.

$D$ iagonal, $A C=20 \mathrm{~cm}$

$B L \perp A C$, such that $B L=8.5 \mathrm{~cm}$

$D M \perp A C$, such that $D M=11.5 \mathrm{~cm}$

$A$ rea of the quadilateral $=(A$ rea of $\Delta D A C)+(A$ rea of $\Delta A C B)$

$=\left[\left(\frac{1}{2} \times A C \times D M\right)+\left(\frac{1}{2} \times A C \times B L\right)\right] \mathrm{cm}^{2}$

$=\left[\left(\frac{1}{2} \times 20 \times 11.5\right)+\left(\frac{1}{2} \times 20 \times 8.5\right)\right] \mathrm{cm}^{2}$

$=(85+115) \mathrm{cm}^{2}$

$=200 \mathrm{~cm}^{2}$