Question

In the given figure, the length of side $$AP$$ is one-fourth the length of side $$DQ$$ and $$AP = BS$$. Also, the length of $$QR$$ is $$5$$ cm.
Find the area of the given polygon.

Answer 1

Correct option is C. $$144\,cm^2$$
$$DQ=LR=16cm$$

$$QR=5cm=DL$$

$$AP=\dfrac{1}{4}QD=\dfrac{16}{4}cm=4cm=BS$$

Area of $$DLRQ\rightarrow QR\times RL$$

$$=5\times 16=80\,cm^3$$

Area of $$\Delta PDQ\rightarrow $$ Area of $$PAD$$ and $$PAQ$$

$$=\dfrac{1}{2}x\times (PA)+\dfrac{1}{2}(16-x)PA$$

$$=\dfrac{1}{2}\times 16\times 4\Rightarrow 32cm^2$$

Similarly area of $$LSR=32cm^2$$

So, Area of polygon $$=80+32+32=144cm^2$$

potion (c) is correct.