Question

4. The parallel sides of a trapezium are 20 m and 30 m and its non-parallel sides
6 m and 8 m. Find the area of the trapezium.
​

Answer 1

Given :-

• Consider a trapezium ABCD

• Parallel sides AB = 20m, CD = 30cm

• Non - parallel sides BC = 8m, AD = 6m

Solution :-

In Trapezium ABCD, Draw CE parallel to AD

Now,

ABED is a parallelogram

Therefore,

AB = ED = 20m

[ Opposite sides of parallelogram are equal ]

And

CD = ED + EC

30 = 20 + EC

EC = 30 - 20 = 10m

Now,

AD = BE = 6m

[ Opposite side of parallelogram ]

Now,

We got all three sides of triangle BEC

BE = 10m, CE = 6m, BC = 8m

Therefore,

Semiperimeter = 10 + 6 + 8 / 2

S = 24/2

S = 12

By using Heron's Formula

$\sqrt{s(s - a)(s - b)(s - c)}$

Put the required values,

$\sqrt{12(12 - 10)(12 - 6)(12 - 8)} \\ \sqrt{12 \times 2 \times 6 \times 4 } \\ \sqrt{24 \times 24} \\ \sqrt{576} \\ 24$

Now,

By using Area of triangle

Area of triangle = 1/2 * Base * Height

24 = 1/2 * 10 * Height

24 = 5 * Height

Height = 24 / 5

Height = 4.8 m

Therefore,

Area of trapezium = 1/2 * h ( a + b)

Area of trapezium = 1/2 * 4.8 ( 20 + 30 )

Area of trapezium = 1/2 * 4.8 * 50

Area of trapezium = 1/2 * 240

Area of trapezium = 120m^2

Hence , The area of trapezium is 120m^2

Answer 2

Solution:-

In trapezium draw a parallel line to its non-parallel sides 8

Now the sides of triangle are 6,8&10

Area of a triangle by heron's formula

S=6+8+10/2

Therefore S=12

Area of a triangle

Area of triangle = 1/2 * Base * Height

24 = 1/2 * 10 * Height

24 = 5 * Height

Height = 24 / 5

Height = 4.8 m

Therefore,

Area of trapezium = 1/2 * h ( a + b)

Area of trapezium = 1/2 * 4.8 ( 20 + 30 )

Area of trapezium = 1/2 * 4.8 * 50

Area of trapezium = 1/2 * 240

Area of trapezium = 120m^2

Hence , The area of trapezium is 120m^2