Answer
The formula for the area (A) of given figure is\[A=ab+\frac{1}{2}\left( c-a \right)b\]
Work Step by Step
Area of given figure will be calculated by finding the area of the rectangle and area of the right triangle given in the figure and then adding the area of that rectangle and triangle. Area is expressed as the space enclosed between a closed figures to the extent of a two-dimensional figure.
It is required to compute the formula for the computation of the area of the given figure.
\[\begin{align}
& \text{Area of right triangle}=\frac{1}{2}\times \text{base}\times \text{height} \\
& =\frac{1}{2}\times \left( c-a \right)\times b \\
& =\frac{1}{2}\times \left( c-a \right)b
\end{align}\]
Compute the area of the rectangle as shown below:
\[\begin{align}
& \text{Area of rectangle}=\text{length}\times \text{breadth} \\
& =a\times b \\
& =ab
\end{align}\]
\[\begin{align}
& \text{Area of given figure}=\text{Area of rectangle}+\text{Area of right triangle} \\
& =ab+\frac{1}{2}\left( c-a \right)b
\end{align}\]
Hence, the area of given figure calculated using the formula is\[ab+\frac{1}{2}\left( c-a \right)b\].
