Question

In the following figures, find the area of the shaded portions:

Answer 1

Step 1: Calculate the area of$△FAE$.

In the figure it is given that, $AF=6cm$ and $AE=10cm$.

So, the area of $△FAE$ is$\frac{1}{2}\times 6\times 10=30c{m}^2$. $[\because$Area of a triangle$=\frac{1}{2}\times$base$\times$height$]$

Therefore, the area of $△FAE$ is$30c{m}^2$.

Step 2: Calculate the area of$△EBC$.

In the figure it is given that, $EB=8cm$ and $BC=10cm$.

So, the area of $△EBC$ is$\frac{1}{2}\times 8\times 10=40c{m}^2$. $[\because$Area of a triangle$=\frac{1}{2}\times$base$\times$height$]$

Therefore, the area of $△EBC$ is$40c{m}^2$.

Step 3: Calculate the area of a rectangle$ABCD$.

In the figure it is given that, $CD=18cm$ and $BC=10cm$.

So, the area of a rectangle $ABCD$ is$18\times 10=180c{m}^2$. $[\because$Area of a rectangle$=$length$\times$breadth$]$

Therefore, the area of rectangle $ABCD$ is $180c{m}^2$.

Step 4: Calculate the area of the shaded region.

According to the figure, the area of the shaded region can be given by:

$$\begin{gathered} ar\left(CDFE\right)=ar(\square ABCD)-ar(△FAE)-ar(△EBC) \\ \Rightarrow ar\left(CDFE\right)=180-30-40 \\ \Rightarrow ar\left(CDFE\right)=110c{m}^2 \end{gathered}$$

Therefore, the area of the shaded region is $110c{m}^2$.