Answer
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.
Solution:
We will be using the formula of area for all figures
(a)
We know that area of 1 square = 1 sq. unit
Now, the total number of squares in the figure = 9
Area of 9 squares = 9 × 1 sq. unit
= 9 sq. units.
Therefore, the area of the given figure is 9 sq. units.
(b)
There are 5 squares in the given figure.
So, Area of 5 squares = 5 × 1 sq. unit
= 5 sq. units
Therefore, the area of the figure is 5 sq. units.
(c)
There are 2 complete squares and 4 half squares in the figure.
So, Area of the figure = 2 × 1 + 4 × 1/2 = 2 + 2 sq. units
= 4 sq. units
Thus, the area of the given figure is 4 sq. units.
(d)
There are 8 squares in the figure.
So, the area of the figure = 8 × 1 sq. unit
= 8 sq. units.
Therefore, the area of the given figure is 8 sq. units.
(e)
There are 10 squares in the figure.
So, the area of the figure = 10 × 1 sq. unit = 10 sq units.
Thus, the area of the figure is 10 sq. units
(f)
There are 2 complete squares and 4 half squares in the figure.
So, Area of the figure = (2 × 1 + 4 × 1/2)
= (2 + 2) sq units
= 4 sq. units.
Thus, area of the given figure is 4 sq. units.
(g)
There are 4 complete squares and 4 half squares in the figure.
So, Area of the given figure = (4 × 1 + 4 × 1/2)
= (4 + 2) sq. units
= 6 sq. units.
Therefore, the area of the given figure is 6 sq. units.
(h)
There are 5 squares in the figure.
So, Area of the figure = 5 × 1 sq. unit
= 5 sq. units.
Thus, the area of the given figure is 5 sq. units.
(i)
There are 9 squares in the figure.
So, Area of the figure = 9 × 1
= 9 sq. units
Thus, the area of the given figure is 9 sq. units.
(j)
There are 2 complete squares and 4 half squares in the figure.
So, Area of the figure =(2 × 1 + 4 × 1/2) sq. units
= (2 + 2) sq. units
= 4 sq. units.
Thus, the area of the figure is 4 sq. units.
(k)
There are 4 complete squares and 2 half squares in the figure.
So, Area of the figure = (4 × 1 + 2 × 1/2) sq. units
= (4 + 1) sq. units
= 5 sq. units
Thus, the area of the figure is 5 sq. units.
(l)
There are 4 complete squares, 3 greater than half squares and 2 half squares in the figure.
So, Area of the figure = (4 × 1 + 3 × 1 + 2 × ½) sq units
= (4 + 3 + 1) sq units
= 8 sq units.
(m)
There are 6 complete squares and 8 greater than half squares in the figure.
So, Area of the figure = (6 × 1 + 8 × 1) sq units
= 6 + 8 sq. units
= 14 sq. units
(n)
There are 9 complete squares and 9 greater than half squares in the figure.
So, Area of the figure = (9 × 1 + 9 × 1) sq units =
(9 + 9) sq units
= 18 sq units.
NCERT Solutions for Class 6 Maths Chapter 10 Exercise 10.2 Question 1
Find the areas of the following figures by counting square:
Summary:
(a) The area of 9 squares = 9 sq units. (b) The area of 5 squares = 5 sq units. (c) The area of 2 complete squares and 4 half squares = 4 sq units. (d) The area of 8 squares = 8 sq units. (e) The area of 10 squares = 10 sq units. (f) The area of 2 complete squares and 4 half squares = 4 sq units. (g) The area of 4 complete squares and 4 half squares = 6 sq units. (h) The area of 5 squares = 5 sq units. (i) The area of 9 squares = 9 sq units. (j) The area of 2 complete squares and 4 half squares = 4 sq units. (k) The area of 4 complete squares and 2 half squares = 5 sq units. (l) The area of 4 complete squares, 3 greater than half squares and 2 half squares = 8 sq units. (m) The area of 6 complete squares and 8 greater than half squares = 14 sq units. (n) The area of 9 complete squares and 9 greater than half squares =18 sq units.
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