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Find the area of the following figure.
 
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seo-qna
Last updated date: 13th Jun 2024
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Answer
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Hint: We have a figure consisting of a rectangle, trapezium, and a parallelogram. We need to find the area of the figure given. So, firstly find the area of rectangle, trapezium, and parallelogram. The formula to find the area of different shapes is given as:
Area of rectangle: ${{A}_{R}}=\left( l\times b \right)$
Area of trapezium: ${{A}_{T}}=\dfrac{1}{2}\times \left( \text{sum of parallel sides} \right)\times \left( \text{height} \right)$
Area of parallelogram: ${{A}_{P}}=\dfrac{1}{2}\times \left( \text{base} \right)\times \left( \text{height} \right)$

Complete step by step answer:
We have a figure consisting of various shapes. So, let us divide them and note down their dimensions.
First, we have a rectangle:
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Length = 8 cm
Breadth = 5 cm
Next, we have a trapezium:
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Height = 5 cm
Side 1 = 7 cm
Side 2 = 6 cm
The last shape we have is a parallelogram:
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Base = 7 cm
Height = 5 cm
So, the area of figure = area of rectangle + area of trapezium + area of parallelogram
i.e. $A={{A}_{R}}+{{A}_{T}}+{{A}_{P}}......(1)$
As we know that: Area of rectangle: ${{A}_{R}}=\left( l\times b \right)$
So, we have:
$\begin{align}
  & {{A}_{R}}=\left( 8\times 5 \right) \\
 & =40c{{m}^{2}}......(2)
\end{align}$
Area of trapezium: ${{A}_{T}}=\dfrac{1}{2}\times \left( \text{sum of parallel sides} \right)\times \left( \text{height} \right)$
So, we have:
$\begin{align}
  & {{A}_{T}}=\dfrac{1}{2}\times \left( 7+6 \right)\times 5 \\
 & =32.5c{{m}^{2}}......(3)
\end{align}$
Area of parallelogram: ${{A}_{P}}=\dfrac{1}{2}\times \left( \text{base} \right)\times \left( \text{height} \right)$
So, we have:
$\begin{align}
  & {{A}_{P}}=\dfrac{1}{2}\times 7\times 5 \\
 & =17.5c{{m}^{2}}......(4)
\end{align}$
So, the area of figure is:
$\begin{align}
  & A=40+32.5+17.5 \\
 & =90c{{m}^{2}}
\end{align}$

Note: It is easier to divide a complex figure into small identifiable figures whose area can be calculated. As for the given figure, it is difficult to tabulate the area of the whole figure, because we do not have a predefined formula for the area of such a complex figure. But when we divided the figure into various small figures that are easily identified, i.e. rectangle, trapezium, and parallelogram. We have the formula for calculating the area of these small figures. So, we can calculate the area of the whole figure by adding all the areas of other small shapes or figures.