Question

The parallel sides of a trapezium are 20 m and 30 m and its non-parallel sides
are 6 m and 8 m. Find the area of the trapezium.
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Answer 1

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

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ANSWER

Draw BE∥AD, then AB∥DE

Hence ABED is a parallelogram

∴AB=DE=20m

AD=BE=8m

EC=DC−DE=30−20=10m

Now, ar△BCE=

s(s−a)(s−b)(s−c)

,s=

2

8+6+10

=12m

∴ar△BCE=

12(12−8)(12−6)(12−10)

=

12×4×6×2

=2×12=24㎡

2

1

×EC×BF=24㎡⇒BF=

10

24×2

=4.8m

∴arABCD=

2

1

×(AB+CD)×BF=

2

1

×(20+30)×4.8

=50×2.4

=120m

2

Answer 2

Given :-

• Length of Parallel sides are 20 m and 30 m
• Length of Non - parallel sides are 6 m and 8 m.

To find :-

• Area of Trapezium.

Assumption :-

• Let ABCD be the Trapezium and
• AB = 20 m
• DC = 30 m
• AD = 6 m
• BC = 8 m

Construction :

• Draw
• AD || BE and AD = BE.

Let's Understand the question before doing :-

Here a Trapezium is given in which two of its parallel sides are given which has the length of 20m and 30m also Its length of its non parallel sides are 6m and 8m respectively. Let's understand by the assumption as a Trapezium ABCD is given in which AB and DC is its parallel sides but not equal and their length is 20 m and 30 m respectively also AD and BC are non parallel sides which has a length of 6m and 8m. But here we don't have height. We need to find its area.

Procedure to do :-

Before finding the Area, we need to find something else of Trapezium that is height. Let's understand how we can find? :- Before that a small construction is needed in which we need to construct AD parallel to BE and also it should be equal to to BE. Therefore it will become Parallelogram as ABDE and one triangle as BEC. We know that Opposites of Parallelogram are equal so AB will be equal to DE as a length of 20m and AD will be equal to BE as a length of 6m. In triangle we have two length only of BE and AC as 6m and 8m respectively. We need to find Length of EC which will be 10m after subtracting EC from DC. By using Heron's formula we will get the area of triangle after putting that Area equal to its formula we will get the height of triangle which also will be the height of Trapezium. For area we will substitute the value in its Formula of Area which will give the area of Trapezium.

________________________________

Solution :-

✬ We have

• AD || BE
• AD = BE = 6m
• Triangle BEC
• Parallelogram ABDE.
• AB = DE = 20m (Parallelogram has equal sides)

✬ In triangle BCE

• BE = 6m
• BC = 8m
• EC = ?

Length of EC is

→ EC = DC - DE

→ EC = 30 - 20

→ EC = 10 m

✬ Area of triangle BCE is

Let a, b, c be the sides, so

• a = 6m
• b = 8m
• c = 10m

Semiperimeter is

→ (a + b + c) / 2

→ (6 + 8 + 10) /2

→ 24 / 2

→ 12 m

Area is

→ √s(s - a)(s - b)(s - c)

→ √ 12(12 - 6)(12 - 8)(12 - 10)

→ √ 12(6) (4) (2)

→ √ 6 × 2 × 6 × 2 × 2 × 2

→ 6 × 2 × 2

→ 24 m²

✬ Height of the Trapezium or Triangle is

→ Area of BCE = 1/2 × Base × Height

→ 24 = 1/2 × EC × Height

→ 24 = 1/2 × 10 × Height

→ Height = (24 × 2) / 10

→ Height = 48 / 10

→ Height = 4.8 m

___________________________________________

✬ Now Area of Trapezium is

${\boxed{\sf{\implies{Area = \frac{1}{2} \times Sum \: of \: Parallel \: sides \times Height}}}}$

${\sf{\implies{Area = \cfrac{1}{2} \times (AB + CD) \times Height}}}$

${\sf{\implies{Area = \cfrac{1}{2} \times (20 + 30) \times 4.8}}}$

${\sf{\implies{Area = \cfrac{1}{2} \times (50) \times 4.8}}}$

${\sf{\implies{Area = {1} \times 25 \times 4.8}}}$

${ \large{ \underline{ \overline{ \boxed{ \red{\sf{\implies{Area = 120 \: {m}^{2} }}}}}}}}$

So, Area of Trapezium is 120m².

_______________________

*Note

• Please Refer to diagram for better understanding.
• Don't be confused because it is Leangth but easily you can understand.
• If it is not clear view then refer to web. Link is given below.
• https://brainly.in/question/32397042