Question Number 149720 by cherokeesay last updated on 06/Aug/21
Answered by mr W last updated on 06/Aug/21
$$\left({R}−\mathrm{1}\right)^{\mathrm{2}} +\left({R}−\mathrm{2}\right)^{\mathrm{2}} ={R}^{\mathrm{2}} \\ $$$${R}^{\mathrm{2}} −\mathrm{6}{R}+\mathrm{5}=\mathrm{0} \\ $$$$\left({R}−\mathrm{5}\right)\left({R}−\mathrm{1}\right)=\mathrm{0} \\ $$$$\Rightarrow{R}=\mathrm{5},\:\mathrm{1}\:\left({rejected}\right) \\ $$$${area}\:{of}\:{semicircle}=\frac{\pi{R}^{\mathrm{2}} }{\mathrm{2}}=\frac{\mathrm{25}\pi}{\mathrm{2}} \\ $$