Question

Find the area of the following figure:

Answer 1

Hint: To find the area of the given figure, we will split the figure into a rectangle and a triangle and then separately calculate their area. For the total area we will add both the areas.

Complete step-by-step answer:
Consider the $\Delta DEF$
From the figure it is clear that
Height of the triangle is 4 cm and
Base of the triangle is $ = 10 - 6 = 4{\text{ cm}}$
As we know that the area of triangle is given by
$ = \dfrac{1}{2} \times base \times height$
Substituting the values of height and base in the above formula
$
   = \dfrac{1}{2} \times 4 \times 4 \\
   = 8{\text{ c}}{{\text{m}}^2} \\
$
Now consider the rectangle ABFC
Length of the rectangle = 10 cm
Breadth of the rectangle = 6 cm
Area of the rectangle is given by
$ = length \times breadth$
Substituting the value of length and breadth in above formula
$
   = 10 \times 6 \\
   = 60\,{\text{c}}{{\text{m}}^2} \\
$
Now total area of the given figure = area of the triangle $ + $ area of the rectangle
$
   = 8 + 60 \\
   = 68{\text{ c}}{{\text{m}}^2} \\
$
Hence, the area of the given figure is $68{\text{ c}}{{\text{m}}^2}$

Note: In order to solve problems related to area calculations in which figures are given such as above try to break the figure in small figures such as rectangle or triangle, then solve the problem in steps as solved above. The most important thing is to remember the formulas of all the important figures.