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

Answer 1

(b) 200 cm²


$$\begin{gathered} \mathrm{Let}ABCD\mathrm{be}\mathrm{a}\mathrm{quadilateral}. \\ D\mathrm{iagonal},AC=20\mathrm{cm} \\ BL\perp AC,\mathrm{such}\mathrm{that}BL=8.5\mathrm{cm} \\ DM\perp AC,\mathrm{such}\mathrm{that}DM=11.5\mathrm{cm} \\ A\mathrm{rea}\mathrm{of}\mathrm{the}\mathrm{quadilateral}=\left(A\mathrm{rea}\mathrm{of}∆DAC\right)+\left(A\mathrm{rea}\mathrm{of}∆ACB\right) \end{gathered}$$
$$\begin{gathered} =\left[\left(\frac{1}{2}\times AC\times DM\right)+\left(\frac{1}{2}\times AC\times BL\right)\right]{\mathrm{cm}}^2 \\ =\left[\left(\frac{1}{2}\times 20\times 11.5\right)+\left(\frac{1}{2}\times 20\times 8.5\right)\right]{\mathrm{cm}}^2 \\ =\left(85+115\right){\mathrm{cm}}^2 \\ =200{\mathrm{cm}}^2 \end{gathered}$$