Question

4. 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.
​

Answer 1

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

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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

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✬ Now Area of Trapezium is

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

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

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

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

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

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

So, Area of Trapezium is 120m²

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Answer 2

Step-by-step explanation:

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

________________________________

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

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✬ Now Area of Trapezium is

So, Area of Trapezium is 120m²

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