Question and Answers Forum

All Questions      Topic List

Geometry Questions

Previous in All Question      Next in All Question      

Previous in Geometry      Next in Geometry      

Question Number 178737 by cherokeesay last updated on 21/Oct/22

Answered by Rasheed.Sindhi last updated on 21/Oct/22

Commented by Rasheed.Sindhi last updated on 21/Oct/22

Let AC=BC=r blue-area=(1/4)πr^2 R=((AB)/2)=((√(r^2 +r^2 ))/2)=(((√2) r)/2) outer circle=πR^2 =π((((√2) r)/2))^2 yello-area=outer circle−blue-area =π((((√2) r)/2))^2 −(1/4)πr^2 =((2πr^2 )/4)−((πr^2 )/4)=((πr^2 )/4) =blue-area

$$\mathrm{Let}\:\mathrm{AC}=\mathrm{BC}=\mathrm{r} \\ $$$$\mathrm{blue}-\mathrm{area}=\frac{\mathrm{1}}{\mathrm{4}}\pi\mathrm{r}^{\mathrm{2}} \\ $$$$\mathrm{R}=\frac{\mathrm{AB}}{\mathrm{2}}=\frac{\sqrt{\mathrm{r}^{\mathrm{2}} +\mathrm{r}^{\mathrm{2}} }}{\mathrm{2}}=\frac{\sqrt{\mathrm{2}}\:\mathrm{r}}{\mathrm{2}} \\ $$$$\mathrm{outer}\:\mathrm{circle}=\pi\mathrm{R}^{\mathrm{2}} =\pi\left(\frac{\sqrt{\mathrm{2}}\:\mathrm{r}}{\mathrm{2}}\right)^{\mathrm{2}} \\ $$$$\mathrm{yello}-\mathrm{area}=\mathrm{outer}\:\mathrm{circle}−\mathrm{blue}-\mathrm{area} \\ $$$$=\pi\left(\frac{\sqrt{\mathrm{2}}\:\mathrm{r}}{\mathrm{2}}\right)^{\mathrm{2}} −\frac{\mathrm{1}}{\mathrm{4}}\pi\mathrm{r}^{\mathrm{2}} =\frac{\mathrm{2}\pi\mathrm{r}^{\mathrm{2}} }{\mathrm{4}}−\frac{\pi\mathrm{r}^{\mathrm{2}} }{\mathrm{4}}=\frac{\pi\mathrm{r}^{\mathrm{2}} }{\mathrm{4}} \\ $$$$\:\:\:\:\:=\mathrm{blue}-\mathrm{area} \\ $$

Commented by cherokeesay last updated on 21/Oct/22

Greet ! thank you

$${Greet}\:!\:{thank}\:{you} \\ $$

Commented by Tawa11 last updated on 21/Oct/22

Great sir

$$\mathrm{Great}\:\mathrm{sir} \\ $$

Answered by HeferH last updated on 21/Oct/22

Blue area: ((π(r(√2))^2 )/4) = ((πr^2 )/2) Yellow area: πr^2 −blue= ((πr^2 )/2) then yellow = blue

$${Blue}\:{area}: \\ $$$$\:\frac{\pi\left({r}\sqrt{\mathrm{2}}\right)^{\mathrm{2}} }{\mathrm{4}}\:=\:\frac{\pi{r}^{\mathrm{2}} }{\mathrm{2}}\: \\ $$$$\:{Yellow}\:{area}: \\ $$$$\:\pi{r}^{\mathrm{2}} \:−{blue}=\:\frac{\pi{r}^{\mathrm{2}} }{\mathrm{2}} \\ $$$$\:{then}\:{yellow}\:=\:{blue} \\ $$

Commented by cherokeesay last updated on 21/Oct/22

Nice ! thank you !

$${Nice}\:!\:{thank}\:{you}\:! \\ $$

Commented by Tawa11 last updated on 21/Oct/22

Great sir

$$\mathrm{Great}\:\mathrm{sir} \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com