A field is in the shape of a trapezium whose parallel sides are 25 m and 10 m. The non-parallel sides are 14 m and 13 m. Find the area of the field.
Solution:
We draw a triangle inside the trapezium and by using Heron’s formula, we can calculate the area of a triangle, and then find the height of the triangle which will also be the height of the trapezium and hence, we will calculate the area of the trapezium.
Heron's formula for the area of a triangle, Area = √s(s - a)(s - b)(s - c)
Where a, b and c are the sides of the triangle, and
s = Semi-perimeter = Half the Perimeter of the triangle = (a + b + c)/2
Given ABCD is a field. Draw CG ⊥ AB from C on AB, and CF parallel to DA.
DC = AF = 10 m, DA = CF = 13 m (opposite sides of parallelogram)
So, FB = 25 - 10 = 15 m
In ∆CFB, a = 15 m, b = 14 m, c = 13 m.
Semi Perimeter(s) = (a + b + c)/2
s = (15 + 14 + 13)/2
s = 42/2
s = 21 m
By using Heron’s formula,
Area of ∆CFB = √s(s - a)(s - b)(s - c)
= √21(21 - 15)(21 - 14)(21 - 13)
= √21 × 6 × 7 × 8
= 84 m2
Also,
Area of ∆CFB = 1/2 × base × height
84 = 1/2 × BF × CG
84 = 1/2 × 15 × CG
CG = (84 × 2)/15
CG = 11.2 m
Area of trapezium ABCD = 1/2 × sum of parallel sides × distance between them
= 1/2 × (AB + DC) × CG
= 1/2 × (25 + 10) × 11.2
= 196 m2
Hence the area of the field is 196 m2.
☛ Check: NCERT Solutions for Class 9 Maths Chapter 12
Video Solution:
A field is in the shape of a trapezium whose parallel sides are 25 m and 10 m. The non-parallel sides are 14 m and 13 m. Find the area of the field
Class 9 Maths NCERT Solutions Chapter 12 Exercise 12.2 Question 9
Summary:
It is given that there is a field is in the shape of a trapezium whose parallel sides are 25 m and 10 m. The non-parallel sides are 14 m and 13 m. We have found that the area of the field is 196 m2.
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