Question

Find the area of the following figure:

Answer 1

Hint: Here, we need to find the area of the figure. We will draw vertical lines to divide the given figure into three rectangles. Then, we will find the areas of the three rectangles. Finally, we will add the areas of the three rectangles to get the area of the given figure.

Formula used: The area of a rectangle is given by the formula \[l \times b\], where \[l\] is the length and \[b\] is the breadth.

Complete step by step solution:
We will divide the given figure into quadrilaterals and calculate the areas of those quadrilaterals.
We will draw vertical lines to divide the figure into three rectangles.
Therefore, the figure becomes

Now, we can observe that the area of the figure is the s of the areas of the three rectangles.
Let the three rectangles be rectangle A, rectangle B, and rectangle C respectively.

The opposite sides of a rectangle are equal.
Therefore, in rectangle C, we get the other sides as 3 cm and 2 cm respectively.

Now, we will find the areas of the three rectangles.
The area of a rectangle is given by the formula \[l \times b\], where \[l\] is the length and \[b\] is the breadth.
Substituting \[l = 4\]cm and \[b = 1\]cm in the formula, we get
Area of rectangle A \[ = 4 \times 1 = 4{\text{ c}}{{\text{m}}^2}\]
Substituting \[l = 3\]cm and \[b = 2\]cm in the formula, we get
Area of rectangle C \[ = 3 \times 2 = 6{\text{ c}}{{\text{m}}^2}\]
From the figure, we can observe that the length of rectangle B is \[7 + 3 = 10\] cm.
Substituting \[l = 10\]cm and \[b = 5\]cm in the formula, we get
Area of rectangle B \[ = 10 \times 5 = 50{\text{ c}}{{\text{m}}^2}\]
Finally, we will add the areas of the three rectangles to get the area of the given figure.
Area of the given figure \[ = \] Area of rectangle A \[ + \] Area of rectangle B \[ + \] Area of rectangle C
Therefore, we get
Area of the given figure \[ = 4 + 50 + 6 = 60{\text{ c}}{{\text{m}}^2}\]

Thus, we get the area of the figure as 60 \[{\text{c}}{{\text{m}}^2}\].

Note: We can also solve the problem by using horizontal lines to divide the figure into three rectangles as shown, and add the areas of those rectangles to get the area of the figure. The answer will remain the same.
Here, the area of rectangle A is 30 square cm, the area of rectangle B is 6 square cm, and the area of rectangle C is 24 square cm. The area of the figure is \[30 + 6 + 24 = 60{\text{ c}}{{\text{m}}^2}\].