Let each of the sides be S.

The formula for the triangle with equal sides:

\(\displaystyle{A}=\frac{{1}}{{2}}{S}^{{2}}{{\sin}^{{2}}\theta}\)

Isolate S:

\(\displaystyle{S}=\sqrt{{\frac{{{2}{A}}}{{{{\sin}^{{2}}\theta}}}}}\)

Substitute \(\displaystyle\theta={112}^{\circ}{\quad\text{and}\quad}{A}={80}{c}{m}^{{2}}\) from the given:

\(\displaystyle{S}=\sqrt{{\frac{{{160}}}{{{{\sin}^{{2}}{\left({112}^{\circ}\right)}}}}}}\)

\(\displaystyle=\frac{{{4}\sqrt{{10}}}}{{\sqrt{{{{\sin}^{{2}}{\left({112}^{\circ}\right)}}}}}}\)

\(\displaystyle=\frac{{{4}\sqrt{{10}}\sqrt{{{{\sin}^{{2}}{\left({112}^{\circ}\right)}}}}}}{{\sqrt{{{{\sin}^{{2}}{\left({112}^{\circ}\right)}}}}\sqrt{{{{\sin}^{{2}}{\left({112}^{\circ}\right)}}}}}}\)

\(\displaystyle=\frac{{{4}\sqrt{{10}}\sqrt{{{{\sin}^{{2}}{\left({112}^{\circ}\right)}}}}}}{{{{\sin}^{{2}}{\left({112}^{\circ}\right)}}}}\)

\(=13.64250...\)