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If AC = 10 cm, AD = 12 cm, BL = 3 cm, CM = 7 cm and EN = 5 cm then what is the area of the following polygon?

Given, AC = 10 cm, AD = 12 cm, BL = 3 cm, CM = 7 cm and EN = 5 cm

$\begin{array}{cl} & \mathrm{Area} \mathrm{of} \mathrm{pentagon} \mathrm{ABCDE}\\ =& (\mathrm{Area} \mathrm{of} \mathrm{\Delta ABC})+(\mathrm{Area} \mathrm{of} \mathrm{\Delta ACD})+(\mathrm{Area} \mathrm{of} \mathrm{\Delta ADE})\end{array}$

$\begin{array}{rcl} & =& (\frac{1}{2}\times \mathrm{AC}\times \mathrm{BL})+(\frac{1}{2}\times \mathrm{AD}\times \mathrm{CM})+(\frac{1}{2}\times \mathrm{AD}\times \mathrm{EN})\end{array}$

$\begin{array}{rcl} & =& \left(\frac{1}{2}\times 10\times 3\right)+\left(\frac{1}{2}\times 12\times 7\right)+\left(\frac{1}{2}\times 12\times 5\right)\end{array}$

$\begin{array}{rcl} & =& 15+42+30\end{array}$

$\begin{array}{rcl} & =& 87 {\mathrm{cm}}^2\end{array}$

Therefore, the area of the polygon ABCDE = 87 cm²