A figure is made up of a triangle and a

Bergen 2021-09-16 Answered

A figure is made up of a triangle and a square, where the triangle's base \(\displaystyle{\left({\underset{{\triangle}}{{{b}}}}\right)}\) is a side of a square \(\displaystyle{\left({\underset{{}}{{{l}}}}\right)}\).
\(\displaystyle{\underset{{\triangle}}{{{h}}}}={8}{c}{m}\)
\(\displaystyle{\underset{{\triangle}}{{{l}}}}={\underset{{\triangle}}{{{s}}}}={10}{c}{m}\)
\(\displaystyle{\underset{{{f}{i}{g}{u}{r}{e}}}{{{P}}}}={56}{c}{m}\)
\(\displaystyle{\underset{{{f}{i}{g}{u}{r}{e}}}{{{A}}}}=?\)

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Expert Answer

Mayme
Answered 2021-09-17 Author has 9455 answers
\(\displaystyle{\underset{{{f}{i}{g}{u}{r}{e}}}{{{A}}}}={\underset{{\boxempty}}{{{A}}}}+{\underset{{\triangle}}{{{A}}}}\)
\(\displaystyle{\underset{{\boxempty}}{{{A}}}}={\underset{{\boxempty}}{{{l}}}}^{{2}}\)
\(\displaystyle{\underset{{\boxempty}}{{{l}}}}=\frac{{{\underset{{{f}{i}{g}{u}{r}{e}}}{{{P}}}}-{2}\times{\underset{{\triangle}}{{{l}}}}}}{{3}}\)
\(\displaystyle=\frac{{{56}-{20}}}{{3}}\)
\(\displaystyle=\frac{{36}}{{3}}\)
=12cm
\(\displaystyle{\underset{{\triangle}}{{{A}}}}=\frac{{1}}{{2}}\times{b}{h}\)
\(\displaystyle=\frac{{1}}{{2}}\times{8}\times{12}\)
\(\displaystyle={48}{c}{m}^{{2}}\)
\(\displaystyle{\underset{{{f}{i}{g}{u}{r}{e}}}{{{A}}}}={12}^{{2}}+{48}\)
=144+48
\(\displaystyle={192}{c}{m}^{{2}}\)
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