Question Number 224246 by mr W last updated on 28/Aug/25
Commented by mr W last updated on 28/Aug/25
$${find}\:{the}\:{area}\:{of}\:{hexagon}. \\ $$
Answered by A5T last updated on 31/Aug/25
Commented by A5T last updated on 31/Aug/25
$$?+\left(\mathrm{4}+?\right)+\left(\mathrm{6}+?\right)−\left(\mathrm{6}+\mathrm{8}+\mathrm{12}\right)=\mathrm{2sh} \\ $$$$\Rightarrow\mathrm{3}?−\mathrm{16}=\mathrm{2sh} \\ $$$$\left(\mathrm{4}+?\right)−\mathrm{8}=\frac{\mathrm{s}}{\mathrm{2}}\left(\mathrm{2h}\right)=\mathrm{sh}\Rightarrow\mathrm{sh}=?−\mathrm{4} \\ $$$$\Rightarrow\mathrm{2sh}=\mathrm{3}?−\mathrm{16}=\mathrm{2}?−\mathrm{8}\Rightarrow?=\mathrm{8} \\ $$$$\Rightarrow\mathrm{Area}\:\mathrm{of}\:\mathrm{hexagon}=\mathrm{6}+\mathrm{8}+\mathrm{12}+\mathrm{8}+\left(\mathrm{4}+\mathrm{8}\right)+\left(\mathrm{6}+\mathrm{8}\right) \\ $$$$=\mathrm{60} \\ $$
Commented by A5T last updated on 31/Aug/25
$$\mathrm{Similar}\:\mathrm{idea}:\:\mathrm{Q206554} \\ $$
Commented by A5T last updated on 31/Aug/25
$$\mathrm{Q207466} \\ $$
Commented by mr W last updated on 31/Aug/25
$${thanks}\:{sir}! \\ $$
Answered by mr W last updated on 31/Aug/25
Commented by mr W last updated on 31/Aug/25
$$\Delta{ABC}=\mathrm{6}+\mathrm{12}−\mathrm{8}=\mathrm{10} \\ $$$${hexagon}'{s}\:{area}\:=\mathrm{6}×\Delta{ABC}=\mathrm{60} \\ $$