Question

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.​

Answer 1

✬ Area of field = 196 m² ✬

Step-by-step explanation:

Given:

• A field is in the shape of trapezium.
• Measure of parallel sides of trapezium are 25 m and 10 m .
• Measure of non parallel sides of trapezium are 14 m and 13 m.

To Find:

• What is the area of field i.e Trapezium?

Solution: Let ABCD be the field in the shape of trapezium in which AB || CD such that

• AB = 25 m and CD = 10 m (Parallel sides)
• BC = 13 m and DA = 14 m (Non-parallel sides)

Construction: Draw CE || DA and CF ⟂ EB . Now clearly ADCE is a Parallelogram.

∴ CE = DA = 14 m and AE = CD = 10 m (Opposite sides of parallogram are equal)

∴ EB = (AB – AE) = (25 – 10) = 15 m.

Now, In ∆EBC we have ,

• EB = 15 m
• BC = 13 m
• CE = 14 m

or, a = 15 m , b = 13 m and c = 14 m

• We have to find the area of ∆EBC by Heron's formula •

★ Semi Perimeter (S) = (a + b + c/2) ★

$\small\implies{\sf }$ S = (15 + 13 + 14/2)

$\small\implies{\sf }$ S = 42/2

$\small\implies{\sf }$ S = 21 m.

★ Heron's Formula ∆ = √S(s – a) (s – b) (s – c) ★

$\small\implies{\sf }$ Area of ∆EBC = √21 (21 – 15) (21 – 13) (21 – 14)

$\small\implies{\sf }$ √21 x 6 x 8 x 7 m²

$\small\implies{\sf }$ √7 x 3 x 3 x 2 x 2 x 2 x 2 x 7 m² [Take commmons]

$\small\implies{\sf }$ (7 x 3 x 2 x 2) m²

$\small\implies{\sf }$ Area (∆EBC) = 84 m²

We know that area of triangle is also (1/2 x Base x Height )

• ∴Area of ∆EBC = ( 1/2 x EB x CF )

$\small\implies{\sf }$ Area (∆EBC) = 1/2 x 15 x CF

$\small\implies{\sf }$ 84 = 1/2 x 15 x CF

$\small\implies{\sf }$ 84 x 2/15 = CF

$\small\implies{\sf }$ 168/15 = CF

$\small\implies{\sf }$ 11.2 m = CF

Hence, The length of CF which is height of both the triangle and trapezium is 11.2 m.

★Area of Trapezium={1/2 x (Sum of parallel sides) x Distance between them}★

∴ Area of trapezium ABCD = {1/2 x (AB + CD) x CF }

$\small\implies{\sf }$ {1/2 x (25 + 10) x 11.2} m²

$\small\implies{\sf }$ (1/2 x 35 x 11.2) m²

$\small\implies{\sf }$ (35 x 5.6) m²

$\small\implies{\sf }$ 196 m²

Hence, The area of field which is in the shape of trapezium is 196 m².