Question

(i) Calculate the area of quad. ABCD, given in Fig. (i).
(ii) Calculate the area of trap. PQRS, given in Fig. (ii).

Answer 1

(i) In $△$BCD,
$$\begin{gathered} {\mathrm{DB}}^2+{\mathrm{BC}}^2={\mathrm{DC}}^2 \\ \Rightarrow {\mathrm{DB}}^2={17}^2-8^2=225 \\ \Rightarrow \mathrm{DB}=15\mathrm{cm} \end{gathered}$$
Ar($△$BCD) = $\frac{1}{2}\times b\times h=\frac{1}{2}\times 8\times 15=60{\mathrm{cm}}^2$
In $△$BAD,
$$\begin{gathered} {\mathrm{DA}}^2+{\mathrm{AB}}^2={\mathrm{DB}}^2 \\ \Rightarrow {\mathrm{AB}}^2={15}^2-9^2=144 \\ \Rightarrow \mathrm{AB}=12\mathrm{cm} \end{gathered}$$
Ar($△$DAB) = $\frac{1}{2}\times b\times h=\frac{1}{2}\times 9\times 12=54{\mathrm{cm}}^2$

Area of quad. ABCD = Ar($△$DAB) + Ar($△$BCD) = 54 + 60 = 114 cm² .

(ii) Area of trap(PQRS) = $\frac{1}{2}\left(8+16\right)\times 8=96{\mathrm{cm}}^2$