Question-219944

Question Number 219944 by Spillover last updated on 04/May/25

Answered by som(math1967) last updated on 04/May/25

Red area=(1/2)π×6^2 −((1/4)π×6^2 +(1/2)×6^2 ) +(1/2)×12×12−((1/4)π×6^2 +(1/2)×6^2 ) =18π−9π−18+72−9π−18 =36cm^2

$${Red}\:{area}=\frac{\mathrm{1}}{\mathrm{2}}\pi×\mathrm{6}^{\mathrm{2}} −\left(\frac{\mathrm{1}}{\mathrm{4}}\pi×\mathrm{6}^{\mathrm{2}} +\frac{\mathrm{1}}{\mathrm{2}}×\mathrm{6}^{\mathrm{2}} \right) \\ $$$$\:+\frac{\mathrm{1}}{\mathrm{2}}×\mathrm{12}×\mathrm{12}−\left(\frac{\mathrm{1}}{\mathrm{4}}\pi×\mathrm{6}^{\mathrm{2}} +\frac{\mathrm{1}}{\mathrm{2}}×\mathrm{6}^{\mathrm{2}} \right) \\ $$$$=\mathrm{18}\pi−\mathrm{9}\pi−\mathrm{18}+\mathrm{72}−\mathrm{9}\pi−\mathrm{18} \\ $$$$=\mathrm{36}{cm}^{\mathrm{2}} \\ $$

Commented by Spillover last updated on 04/May/25

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

Answered by mehdee7396 last updated on 04/May/25

S=(1/2)×36+(36−(1/4)×36π)+((1/4)×36π−(1/2)×36) =36 ✓

$${S}=\frac{\mathrm{1}}{\mathrm{2}}×\mathrm{36}+\left(\mathrm{36}−\frac{\mathrm{1}}{\mathrm{4}}×\mathrm{36}\pi\right)+\left(\frac{\mathrm{1}}{\mathrm{4}}×\mathrm{36}\pi−\frac{\mathrm{1}}{\mathrm{2}}×\mathrm{36}\right) \\ $$$$=\mathrm{36}\:\checkmark \\ $$

Commented by mehdee7396 last updated on 04/May/25