To find length and width, you use the distance formula:
\(d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}\)
For the length, you use the points \((-2, 3)\) and \((1, 5)\)
\(d=\sqrt{(1-(-2))^{2}+(5-3)^{2}}\)
\(=\sqrt{3^{2}+2^{2}}\)
\(=\sqrt{9+4}\)
\(=\sqrt{13}\)
For the width, you use the points \((-2, 3)\) and \((2, -3)\)
\(d=\sqrt{(2-(-2))^{2}+(-3-3)^{2}}\)
\(=\sqrt{4^{2}+(-6)^{2}}\)
\(=\sqrt{16+36}\)
\(=\sqrt{52}\)
\(=2\sqrt{13}\)
So we multiply:
\(\sqrt{13}*2\sqrt{13}=2*13=26\)
which is the area.
