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Question Number 142604 by Engr_Jidda last updated on 02/Jun/21

Answered by mr W last updated on 02/Jun/21

a=14  r_1 =b=10.5  r_2 =(√(a^2 +b^2 ))−b  r_3 =b−r_2 =2b−(√(a^2 +b^2 ))  α=tan^(−1) (b/a)  S=((ab)/2)−((r_1 ^2 α)/2)−((r_2 ^2 ((π/2)−α))/2)−((πr_3 ^2 )/4)

$${a}=\mathrm{14} \\ $$$${r}_{\mathrm{1}} ={b}=\mathrm{10}.\mathrm{5} \\ $$$${r}_{\mathrm{2}} =\sqrt{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} }−{b} \\ $$$${r}_{\mathrm{3}} ={b}−{r}_{\mathrm{2}} =\mathrm{2}{b}−\sqrt{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} } \\ $$$$\alpha=\mathrm{tan}^{−\mathrm{1}} \frac{{b}}{{a}} \\ $$$${S}=\frac{{ab}}{\mathrm{2}}−\frac{{r}_{\mathrm{1}} ^{\mathrm{2}} \alpha}{\mathrm{2}}−\frac{{r}_{\mathrm{2}} ^{\mathrm{2}} \left(\frac{\pi}{\mathrm{2}}−\alpha\right)}{\mathrm{2}}−\frac{\pi{r}_{\mathrm{3}} ^{\mathrm{2}} }{\mathrm{4}} \\ $$

Commented by Engr_Jidda last updated on 03/Jun/21

thank you sir

$${thank}\:{you}\:{sir} \\ $$

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