Question

You are given the following two figures. Find the area of both the figures.

Answer 1

Hint:For this question we will start with first analyzing the figures and divide it into simple figures and then find the area and add them. We will only divide them into figures like rectangles and square and apply the formula for the area of a rectangle which is $\left( length\times breadth \right)$ and the area of square ${{\left( side \right)}^{2}}$ and get the answer.

Complete step by step answer:

Let’s take the first figure into consideration, so we have:

Now to find the area of the given polygon, we will now divide it into three different parts as follows:

From the obtained figure we see that the area of the polygon is equal to the sum all the three parts, now we see that first figure that is $I$ is a rectangle of the measurements $5\text{ cm }\times \text{ }2\text{ cm}$ and the second figure that is $II$ is a square of the side $2\text{ cm}$ and the final figure that is $III$ is a rectangle of the measurements: $5\text{ cm }\times \text{ }2\text{ cm}$.
Now the area of the polygon will be equal to $Area\left( I+II+III \right)$
 $\begin{align}
  & \Rightarrow Area\left( I+II+III \right)=\left( \left( 5\times 2 \right)+\left( 2\times 2 \right)+\left( 5\times 2 \right) \right) \\
 & \Rightarrow Area\left( I+II+III \right)=10+4+10=24\text{ c}{{\text{m}}^{2}} \\
\end{align}$
Therefore, the area of first figure is $24\text{ c}{{\text{m}}^{2}}$
Now, let’s take the second figure into consideration, so we have:

Now to find the area of the given polygon, we will now divide it into two different parts as follows:

From the obtained figure we see that the area of the polygon is equal to the sum all the two parts, now we see that first figure that is $I$ is a rectangle of the measurements $\text{2 cm }\times \text{ 3 cm}$ and the second figure that is $II$ is a rectangle of the measurements: $\left( 3+2 \right)\text{cm }\times \text{ }2\text{ cm}=5\text{ cm }\times \text{ }2\text{ cm}$.
Now the area of the polygon will be equal to $Area\left( I+II \right)$
 $\begin{align}
  & \Rightarrow Area\left( I+II \right)=\left( \left( 2\times 3 \right)+\left( 5\times 2 \right) \right) \\
 & \Rightarrow Area\left( I+II \right)=6+10=16\text{ c}{{\text{m}}^{2}} \\
\end{align}$
Therefore, the area of first figure is $\text{16 c}{{\text{m}}^{2}}$

Note:
 Always draw all the figures before and after the division for a better understanding of the examiner. Student must mention all the measurements of sides after they divide the figure and also it is necessary to mention the unit of area that is square units. In this case it is $c{{m}^{2}}$. Students can also try to complete the figures such that it makes a complete rectangle and then find its area. Then, they can subtract the area of the unshaded region from it to get the area of the shaded region, which is in fact the required area of the figure.