Question Number 154138 by iloveisrael last updated on 14/Sep/21
Answered by EDWIN88 last updated on 14/Sep/21
Commented by EDWIN88 last updated on 14/Sep/21
$$\Rightarrow{Red}\:{area}\:=\:\frac{\mathrm{1}}{\mathrm{2}}×\frac{\mathrm{18}}{\mathrm{7}}×\frac{\mathrm{24}}{\mathrm{7}}=\frac{\mathrm{216}}{\mathrm{49}} \\ $$$$\left(\bullet\right)\:\frac{{h}}{\mathrm{6}}=\frac{\mathrm{8}−\mathrm{2}{R}}{\mathrm{8}} \\ $$$$\Rightarrow\frac{{h}}{\mathrm{3}}=\frac{\mathrm{4}−\frac{\mathrm{24}}{\mathrm{7}}}{\mathrm{2}}\:;\:{h}=\frac{\mathrm{3}\left(\frac{\mathrm{4}}{\mathrm{7}}\right)}{\mathrm{2}}=\frac{\mathrm{6}}{\mathrm{7}} \\ $$$$\Rightarrow{orange}\:{area}\:=\:\frac{\mathrm{1}}{\mathrm{2}}×\left(\mathrm{8}−\frac{\mathrm{24}}{\mathrm{7}}\right)×\left(\frac{\mathrm{24}}{\mathrm{7}}\right)−\frac{\mathrm{1}}{\mathrm{2}}×\left(\mathrm{8}−\frac{\mathrm{24}}{\mathrm{7}}\right)×\frac{\mathrm{6}}{\mathrm{7}} \\ $$$${orange}\:{area}\:=\frac{\mathrm{1}}{\mathrm{2}}×\frac{\mathrm{32}}{\mathrm{7}}\left(\frac{\mathrm{24}}{\mathrm{7}}−\frac{\mathrm{6}}{\mathrm{7}}\right) \\ $$$${orange}\:{area}\:=\:\frac{\mathrm{16}}{\mathrm{7}}×\frac{\mathrm{18}}{\:\mathrm{7}}=\frac{\mathrm{288}}{\mathrm{49}} \\ $$$${then}\:\frac{{red}\:{area}}{{orange}\:{area}}=\frac{\mathrm{216}}{\mathrm{49}}×\frac{\mathrm{49}}{\mathrm{288}}=\frac{\mathrm{3}}{\mathrm{4}} \\ $$