Overlap of Congruent Triangles

Due to symmetry, the overlapped figure is made of 6 congruent triangles as shown above. The overlap with an area of $\text{12 cm}^2$ is made up of two of such triangles, therefore each triangle is $\text{6 cm}^2$ . $\triangle ABC$ is made of four such triangle and hence has an area of $6 \times 4 = \boxed{\text{24 cm}^2}$ .

Let $|\overline {AB}|=a$ and $|\overline {FC}|=h$ . Then the area of the overlapped region is $2\times \dfrac{1}{2}\times \dfrac{a}{2}\times \dfrac{h}{2}=12$ , or $\dfrac{1}{2}ah=24$ . Therefore area of $\triangle {ABC}$ is $\boxed {24 cm^2}$