Question

the parallel sides of trapezium are 20m and 30m and its non-parallel sides are 6m and 8m . find the area of trapezium

Answer 1

In a trapezium draw a parallel line to its non-parallel side 8.
Now here the sides of triangle are 6,8 and 10
Area of triangle by heron's formula
S=6+8+10/2
S=12
Area of triangle,
√S(S-A)(S-B)(S-C)
√12(12-6)(12-8)(12-10)
√12×6×4×2
=24
Area of triangle=24
1/2×B×H=24
H=24×2÷10
H=4.8
Now area of trapezium,
1/2(sum of parallel side)h
1/2(20+30)4.8
50×4.8/2
50×2.4
120m^2
So the area of trapezium =120m^2

Answer 2

Hey Mate !

Ans. -----》 Given = AB = 20 m
CD = 30 m
AD = 6m
BC = 8 m
AB // CD

Construction = Draw AE // BC

ABCE is a //gm.
Therefore , EC = 20m
And , In Triangle ADE
AE = 8 m
DE = 10m
a = 6 m , b = 8 m , c = 10 m

Now , In Triangle ADE
S ( semi perimeter ) = a+b+c = 6+8+10 = 24 = 12m
______ ______ ___
2 2 2

$\sqrt{s(s - a)(s - b)(s - c) }$
$\sqrt{12(12 - 6)(12 - 8)(12 - 10)}$
$\sqrt{12 \times 6 \times 4 \times 2}$
( Factorise the numbers )

$\sqrt{2 \times 2 \times 3 \times 3 \times 2 \times 2 \times 2 \times 2}$

( Make pairs )

$2 \times 3 \times 2 \times 2$

${24}m^{2}$
Now ,
Area of Triangle = 1/2 × base × height
24 = 1/2 × 10 × h
24 × 2 = h
______
10

h = 4.8 m

So ,
Area of Trapezium = 1/2 × ( sum of the // sides ) × h
= 1/2 × ( 20 + 30 ) × 4.8
= 1/2 × 50 × 4.8
= 25 × 4.8
= 120 m²
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