ABC26GN4450 · Area

$AD=\sqrt{4^{2}+6^{2}}\ \text{cm}=\sqrt{52}\ \text{cm}=2\sqrt{13}\ \text{cm}=(2 \times 3.6)\ \text{cm}=7.2\ \text{cm}$. $BC=AD=7.2\ \text{cm}$. Area of the whole figure $=\text{area}(\triangle AED)+\text{area}(\text{rect. } ABCD)+\text{area}(\triangle BFC)$ $=\left[\left(\frac{1}{2} \times 4 \times 6\right)+(12 \times 7.2)+\left(\frac{1}{2} \times 4 \times 6\right)\right]\ \text{cm}^2$ $=(24+86.4)\ \text{cm}^2=110.4\ \text{cm}^2$.