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class 8 ncert chater ii exercise 11.2
question 4
Answers
Answer:
Given :
Given :Diagonal of quadrilateral = 24 m and perpendicular dropped on it (diagonal) from the remaining opposite vertices are 8 m and 13 m.
Given :Diagonal of quadrilateral = 24 m and perpendicular dropped on it (diagonal) from the remaining opposite vertices are 8 m and 13 m.(As shown in figure)
Given :Diagonal of quadrilateral = 24 m and perpendicular dropped on it (diagonal) from the remaining opposite vertices are 8 m and 13 m.(As shown in figure)Find :
Given :Diagonal of quadrilateral = 24 m and perpendicular dropped on it (diagonal) from the remaining opposite vertices are 8 m and 13 m.(As shown in figure)Find :Area of the Quadrilateral.
Solution :
We know that
Area of quadrilateral = 1/2 × diagonal × (Sum of perpendicular on the quadrilateral from remaining opposite vertices)
Assume a quadrilateral ABCD such that
BD = diagonal of quadrilateral
AM and CN = perpendiculars on the diagonal
We have
Diagonal = BD = 24 m
Perpendicular on the quadrilateral (AM and AN) = 8 m and 13 m
Substitute the known values in above formula. To find the value of area of field (quadrilateral).
→ 1/2 × 24 × (8 + 13)
→ 12 × 21
→ 252 m²
∴ Area of quadrilateral is 252 m².
hope this helps you
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NCERT Solutions for Class 8 Maths Chapter 11 Mensuration Ex 11.2
October 4, 2019 by Sastry CBSE
NCERT Solutions for Class 8 Maths Chapter 11 Mensuration Ex 11.2
Class 8 Maths Mensuration Exercise 11.1
Class 8 Maths Mensuration Exercise 11.2
Class 8 Maths Mensuration Exercise 11.3
Class 8 Maths Mensuration Exercise 11.4
Mensuration Class 8 Extra Questions
NCERT Solutions for Class 8 Maths Chapter 11 Mensuration Exercise 11.2
Ex 11.2 Class 8 Maths 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.
NCERT Solutions for Class 8 Maths Chapter 11 Mensuration Ex 11.2 Q1
Solution:
Area of the trapezium = 12 × (a + b) × h
= 12 × (1.2 + 1) × 0.8
= 12 × 2.2 × 0.8
= 0.88 m2
Hence, the required area = 0.88 m2
Ex 11.2 Class 8 Maths 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 sides.
Solution:
Given: Area of trapezium = 34 cm2
Length of one of the parallel sides a = 10 cm
height h = 4 cm
Area of the trapezium = 12 × (a + b) × h
34 = 12 × (10 + b) × 4
⇒ 34 = (10 + b) × 2
⇒ 17 = 10 + b
⇒ b = 17 – 10 = 7 cm
Hence, the required length = 7 cm.
Ex 11.2 Class 8 Maths 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.
NCERT Solutions for Class 8 Maths Chapter 11 Mensuration Ex 11.2 Q3
Solution:
Given:
AB + BC + CD + DA = 120 m .
BC = 48 m, CD = 17 m, AD = 40 m
AB = 120 m – (48 m + 17 m + 40 m) = 120 – 105 m = 15 m
Area of the trapezium ABCD = 12 × (BC + AD) × AB
= 12 × (48 + 40) × 15
= 12 × 88 × 15
= 44 × 15 = 660 m2.
Hence, the required area = 660 m2