# A figure is made up of a triangle and a

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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Mayme
$$\displaystyle{\underset{{{f}{i}{g}{u}{r}{e}}}{{{A}}}}={\underset{{\boxempty}}{{{A}}}}+{\underset{{\triangle}}{{{A}}}}$$
$$\displaystyle{\underset{{\boxempty}}{{{A}}}}={\underset{{\boxempty}}{{{l}}}}^{{2}}$$
$$\displaystyle{\underset{{\boxempty}}{{{l}}}}=\frac{{{\underset{{{f}{i}{g}{u}{r}{e}}}{{{P}}}}-{2}\times{\underset{{\triangle}}{{{l}}}}}}{{3}}$$
$$\displaystyle=\frac{{{56}-{20}}}{{3}}$$
$$\displaystyle=\frac{{36}}{{3}}$$
=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
$$\displaystyle={192}{c}{m}^{{2}}$$