Answer
The area of the shaded region of the given figure is\[192\text{ c}{{\text{m}}^{2}}\].
Work Step by Step
We have to find the area of the shaded region in the given figure. It can be computed by subtracting the area of the smaller triangle, with height equal to \[6\text{ cm}\],from the bigger triangle, that has the height equal to \[12\text{ cm}+6\text{ cm}=18\text{ cm}\].
According to this formula, the area of the bigger triangle, with base equal to \[8+8+8=24\text{ cm}\]and height equal to \[18\text{ cm}\]will be:
\[\begin{align}
& {{A}_{1}}=\frac{1}{2}\times 24\times 18 \\
& \text{ =12}\times 18 \\
& \text{ =}216c{{m}^{2}} \\
\end{align}\]
The area of the smaller triangle, with base equal to \[8\text{cm}\]and height equal to \[6\text{cm}\]will be:
\[\begin{align}
& {{A}_{2}}=\frac{1}{2}\times 8\times 6 \\
& \text{ =4}\times 6 \\
& \text{ =24}c{{m}^{2}} \\
\end{align}\]
The area of the shaded region will be:
\[\begin{align}
& A={{A}_{1}}-{{A}_{2}} \\
& \text{ =}216-24 \\
& \text{ =}192c{{m}^{2}} \\
\end{align}\]
Hence, the area of the shaded region of the given figure is\[192\text{ c}{{\text{m}}^{2}}\].
