Answer
The area of the given figure, according to the variables shown is\[A=b\left( a+\frac{1}{2}b \right)\].
Work Step by Step
We have to find a formula for the area of the given figure. The figure consists of a rectangle attached to an isosceles triangle.
The rectangle has sides a and b, and the right angled isosceles triangle has two equal sides of length b.
For finding out the formula, we have to add the formulas of the two figures that makes up the figure.
Area of a rectangle with length as a and breadth as b is as follows:
\[{{A}_{1}}=ab\]
Area of the right angled isosceles triangle with equal sides of length b is as follows:
\[\begin{align}
& {{A}_{2}}=\frac{1}{2}b\times b \\
& \text{ =}\frac{1}{2}{{b}^{2}} \\
\end{align}\]
So, the total area of the figure will be as follows:
\[\begin{align}
& A={{A}_{1}}+{{A}_{2}} \\
& =ab+\frac{1}{2}{{b}^{2}} \\
& =b\left( a+\frac{1}{2}b \right)
\end{align}\]
Hence, the area of the given figure according to the variables shown is\[A=b\left( a+\frac{1}{2}b \right)\].
