Class 8 CBSE Mathematics - NCERT Solutions of Chapter 11 Mensuration Exercise 11.2

 

CBSE Class 8, Mathematics - Mensuration

Chapter 11, NCERT Mathematics

NCERT solutions of Mensuration Exercise 11.2

Question 1:
The shape of the top surface of a table is a trapezium. Find its area if its parallel sides are 1 m and 1.2 m and perpendicular distance between them is 0.8 m.
Class 8 CBSE Mathematics - NCERT Solutions of Chapter 11 Mensuration Exercise 11.2, Question 1

Solution:
Class 8 CBSE Mathematics - NCERT Solutions of Chapter 11 Mensuration Exercise 11.2, Question 1






Question 2:
The area of a trapezium is 34 cm2 and the length of one of the parallel sides is 10 cm and its height is 4 cm. Find the length of the other parallel side.
Solution:
It is given that, area of trapezium = 34 cm2 and height = 4 cm
Let the lengths of parallel sides are b­1 and b2. We know that,
Area of trapezium = 1/2(b1 + b2) × h  
[h = distance between the parallel sides]
So, 34 = 1/2 (10 + b2) x 4
Or, 34 = (10 + b2) x 2
Or, 17 = 10 + b2
Or, b2 = 7 cm
Thus, the length of the other parallel side is 7 cm.

Question 3:
Length of the fence of a trapezium shaped field ABCD is 120 m. If BC = 48 m, CD = 17 m and AD = 40 m, find the area of this field. Side AB is perpendicular to the parallel sides AD and BC.
CBSE Class 8 Mathematics - NCERT Solutions of Chapter 11 Mensuration Exercise 11.2, Question 3

Solution:
Length of the fence of trapezium ABCD = AB + BC + CD + DA
120 m = AB + 48 m + 17 m + 40 m
AB = 120 m − 105 m = 15 m
CBSE Class 8 Mathematics - NCERT Solutions of Chapter 11 Mensuration Exercise 11.2, Question 3










Question 4:
The diagonal of a quadrilateral shaped field is 24 m and the perpendiculars dropped on it from the remaining opposite vertices are 8 m and 13 m. Find the area of the field.
CBSE Class 8 Mathematics - NCERT Solutions of Chapter 11 Mensuration Exercise 11.2, Question 4


Solution:
Given that the length of the diagonal, d = 24 m
Length of the perpendiculars, h1 and h2, from the opposite vertices to the diagonal are
h1 = 8 m and h2 = 13 m
CBSE Class 8 Mathematics - NCERT Solutions of Chapter 11 Mensuration Exercise 11.2, Question 4















Question 5:
The diagonals of a rhombus are 7.5 cm and 12 cm. Find its area.
Solution:
CBSE NCERT Solutions of Class 8 Math Mensuration Exercise 11.2, Question 5













Question 6:
Find the area of a rhombus whose side is 6 cm and whose altitude is 4 cm. If one of its diagonals is 8 cm long, find the length of the other diagonal.
Solution:
Let the length of the other diagonal of the rhombus be x.
Area of the given rhombus = Base × Height = 6 cm × 4 cm = 24 cm2
Also, area of rhombus = 1/2(Product of its diagonals)
CBSE NCERT Solutions of Class 8 Math Mensuration Exercise 11.2, Question 6











Question 7:
The floor of a building consists of 3000 tiles which are rhombus shaped and each of its diagonals are 45 cm and 30 cm in length. Find the total cost of polishing the floor, if the cost per m2 is Rs 4.
Solution:
Area of rhombus = 1/2(Product of its diagonals)
Hence, area of each tile





= 675 cm2
Area of 3000 tiles = (675 × 3000) cm2 = 2025000 cm2 = 202.5 m2
Cost of polishing 202.5 m2 area @ Rs 4 per m2
= Rs (4 × 202.5) = Rs 810
Thus, the cost of polishing the floor is Rs 810.

Question 8:
Mohan wants to buy a trapezium shaped field. Its side along the river is parallel to and twice the side along the road. It the area of this field is 10500 m2 and the perpendicular distance between the two parallel sides is 100 m, find the length of the side along the river.
CBSE NCERT Solutions of Class VIII Math Mensuration Exercise 11.2, Question 8

Solution:
Let us assume the length of the field along the road is l m. So according to the given condition, the length of the field along the river will be 2l m.
Area of trapezium = 1/2(Sum of parallel sides) (Distance between the parallel sides)
CBSE NCERT Solutions of Class VIII Math Mensuration Exercise 11.2, Question 8











Question 9:
Top surface of a raised platform is in the shape of a regular octagon as shown in the figure. Find the area of the octagonal surface.
CBSE NCERT Solutions of Class VIII Math Mensuration Exercise 11.2, Question 9

Solution:











Since the shape of the platform is a regular octagon (each side = 5 cm),
So, area of trapezium ABCH = area of trapezium DEFG










Question 10:
There is a pentagonal shaped park as shown in the figure.
For finding its area Jyoti and Kavita divided it in two different ways. Find the area of this park using both ways. Can you suggest some other way of finding its area?
Class VIII, Mensuration - Mathematics CBSE Guide NCERT Solution

Solution:
Jyoti’s diagram:
 Mensuration - 8th CBSE Math NCERT Solutions of Chapter 11 Exercise 11.2 Question 10














Kavita’s diagram:
 Mensuration - 8th CBSE Math NCERT Solutions of Chapter 11 Exercise 11.2 Question 10






















Question 11:
Diagram of the adjacent picture frame has outer dimensions = 24 cm × 28 cm and inner dimensions 16 cm × 20 cm. Find the area of each section of the frame, if the width of each section is same.
Class VIII, Mensuration - Mathematics CBSE Guide NCERT Solution

Solution:
Area of outer frame in the picture = length x breadth
                                       = 28 x 24 = 672 cm2
Area of inner frame in the picture = l x b
                                       = 16 x 20 = 320 cm2
Hence, area of remaining portion = 672 - 320 = 352 cm2

So, area of each section = 352 ÷ 4 = 88 cm2

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