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Question Number 186442 by Mingma last updated on 04/Feb/23

Answered by HeferH last updated on 04/Feb/23

Commented by HeferH last updated on 04/Feb/23

(((11)/2))^2 −r^2  = r^2 −4 + ((3/2))^2    r^2  = 16   Yellow = ((r^2 π)/2) = 8π u^2

$$\left(\frac{\mathrm{11}}{\mathrm{2}}\right)^{\mathrm{2}} −{r}^{\mathrm{2}} \:=\:{r}^{\mathrm{2}} −\mathrm{4}\:+\:\left(\frac{\mathrm{3}}{\mathrm{2}}\right)^{\mathrm{2}} \\ $$$$\:{r}^{\mathrm{2}} \:=\:\mathrm{16} \\ $$$$\:{Yellow}\:=\:\frac{{r}^{\mathrm{2}} \pi}{\mathrm{2}}\:=\:\mathrm{8}\pi\:{u}^{\mathrm{2}} \\ $$

Answered by mr W last updated on 04/Feb/23

r^2 =(((a+b+c)b+2ac)/4)     =(((5+4+2)×4+2×5×2)/4)=16  yellow area=((πr^2 )/2)=8π

$${r}^{\mathrm{2}} =\frac{\left({a}+{b}+{c}\right){b}+\mathrm{2}{ac}}{\mathrm{4}} \\ $$$$\:\:\:=\frac{\left(\mathrm{5}+\mathrm{4}+\mathrm{2}\right)×\mathrm{4}+\mathrm{2}×\mathrm{5}×\mathrm{2}}{\mathrm{4}}=\mathrm{16} \\ $$$${yellow}\:{area}=\frac{\pi{r}^{\mathrm{2}} }{\mathrm{2}}=\mathrm{8}\pi \\ $$

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