Question Number 216106 by mr W last updated on 27/Jan/25
Commented by mr W last updated on 27/Jan/25
$${three}\:{squares}\:{with}\:{side}\:{lengthes} \\ $$$${a},{b},{c}\:{respectively}. \\ $$$${find}\:{the}\:{area}\:{of}\:{the}\:{red}\:{triangle}. \\ $$
Answered by A5T last updated on 27/Jan/25
![[Red]=(((a+c)(a+b+c))/2)−(a^2 /2)−(((b+c)c)/2)=((a(b+2c))/2)](https://www.tinkutara.com/question/Q216108.png)
$$\left[\mathrm{Red}\right]=\frac{\left(\mathrm{a}+\mathrm{c}\right)\left(\mathrm{a}+\mathrm{b}+\mathrm{c}\right)}{\mathrm{2}}−\frac{\mathrm{a}^{\mathrm{2}} }{\mathrm{2}}−\frac{\left(\mathrm{b}+\mathrm{c}\right)\mathrm{c}}{\mathrm{2}}=\frac{\mathrm{a}\left(\mathrm{b}+\mathrm{2c}\right)}{\mathrm{2}} \\ $$
Commented by mr W last updated on 27/Jan/25
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Answered by mr W last updated on 27/Jan/25
Commented by mr W last updated on 27/Jan/25
$${red}\:{area}={hatched}\:{area}=\frac{{a}\left({b}+\mathrm{2}{c}\right)}{\mathrm{2}} \\ $$