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.
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
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.
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
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.
☛ Related Questions:
- A triangle and a parallelogram have the same base and the same area. If the sides of the triangle are 26 cm, 28 cm, and 30 cm, and the parallelogram stands on the base 28 cm, find the height of the parallelogram.
- A rhombus shaped field has green grass for 18 cows to graze. If each side of the rhombus is 30 m and its longer diagonal is 48 m, how much area of grass field will each cow be getting?
- An umbrella is made by stitching 10 triangular pieces of cloth of two different colours (See Fig. 12.16), each piece measuring 20 cm, 50 cm, and 50 cm. How much cloth of each colour is required for the umbrella?
- A kite in the shape of a square with a diagonal 32 cm and an isosceles triangle of base 8 cm and sides 6 cm each is to be made of three different shades as shown in Fig. 12.17 How much paper of each shade has been used in it?