Question Number 205461 by mr W last updated on 21/Mar/24
Commented by mr W last updated on 21/Mar/24
$${find}\:{the}\:{area}\:{of}\:{the}\:{third}\:{part}\: \\ $$$${between}\:{two}\:{squares}. \\ $$
Answered by mr W last updated on 22/Mar/24
Commented by mr W last updated on 22/Mar/24
$${green}\:{hatched}\:{area}=\mathrm{250}+\mathrm{150}=\mathrm{400} \\ $$$${blue}\:{hatched}\:{area}={unknown}\:{area}\:? \\ $$$${due}\:{to}\:{symmetry}\: \\ $$$${blue}\:{hatched}\:{area}={green}\:{hatched}\:{area} \\ $$$$\Rightarrow?=\mathrm{250}+\mathrm{150}=\mathrm{400}\:\checkmark \\ $$
Answered by A5T last updated on 21/Mar/24
$$\frac{\left({a}+{s}\right){e}}{\mathrm{2}}=\mathrm{250};\frac{\left({a}+{s}\right){d}}{\mathrm{2}}=\mathrm{150} \\ $$$$\Rightarrow\frac{\left({a}+{s}\right)\left({d}+{e}\right)}{\mathrm{2}}=\mathrm{400}\Rightarrow{s}^{\mathrm{2}} −{a}^{\mathrm{2}} =\mathrm{800} \\ $$$${a}^{\mathrm{2}} +\mathrm{400}+?={s}^{\mathrm{2}} \Rightarrow{s}^{\mathrm{2}} −{a}^{\mathrm{2}} =\mathrm{400}+?=\mathrm{800}\Rightarrow?=\mathrm{400}{cm}^{\mathrm{2}} \\ $$
Commented by mr W last updated on 22/Mar/24
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Commented by A5T last updated on 21/Mar/24
