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Find the approximate area of a trapezium whose parallel sides are 22 cm, 12 cm and the other sides are 8 cm and 6 cm.
- a)73.3 sq. cm.
- b)81.6 sq. cm.
- c)31.3 sq. cm.
- d)75.5 sq. cm.
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Find the approximate area of a trapezium whose parallel sides are 22 c...
Consider the trapezium ABCD,
where AB = 6 cm, BC = 12 cm, CD = 8 cm and AD = 22 cm.
Draw a line from C parallel to AB at E such that ABCE is a parallelogram.
∴ CE = AB = 6 cm and AE = BC = 12 cm.
AD = AE + ED
⇒ ED = AD – AE
⇒ ED = 22 – 12 = 10 cm.
Area of Trapezium ABCD = Area of Parallelogram ABCE + Area of ΔCED
Draw a line through C to ED such that CF is perpendicular to ED.
Area of ΔCED:
From Heron’s formulae,
Δ CED = √[(s) (s - a) (s - b) (s - c)], where s = (a + b + c)/2 and a, b, c are side of the triangle.
In this case, a = 6; b = 8 and c = 10
⇒ s = 24/2 = 12
Area of ΔCED = √(12 × 6 × 4 × 2)
⇒ Area of ΔCED = √(576) = 24 sq. cm.
Area of ΔCED = (1/2) × ED × CF
⇒ 24 = (1/2) × 10 × CF
⇒ CF = 4.8 cm.
Area of Parallelogram ABCE = AE × CF
⇒ Area of Parallelogram ABCE = 12 × 4.8 = 57.6 sq. cm.
Area of trapezium ABCD = Area of parallelogram ABCE + Area of ΔCED
⇒ Area of trapezium ABCD = 57.6 + 24 = 81.6 sq. cm.
∴ Approximate area of the trapezium = 81.6 sq. cm.
Most Upvoted Answer
Find the approximate area of a trapezium whose parallel sides are 22 c...
Finding the Area of Trapezium
Given:
Parallel sides of trapezium = 22 cm, 12 cm
Other sides of trapezium = 8 cm, 6 cm
To find: Approximate area of trapezium
Formula for area of trapezium:
Area = 1/2 × (sum of parallel sides) × (distance between parallel sides)
Steps to solve:
1. Find the distance between parallel sides:
We can use Pythagoras theorem to find the distance between parallel sides.
a² = b² + c²
where a = difference between parallel sides, b and c = lengths of other sides
Substituting the given values, we get:
a² = 8² - 6²
a² = 64 - 36
a² = 28
a ≈ 5.29 cm
Therefore, the distance between parallel sides is approximately 5.29 cm.
2. Substitute the values in the formula for area:
Area = 1/2 × (22 + 12) × (5.29)
Area = 1/2 × 34 × 5.29
Area ≈ 81.6 sq. cm
Therefore, the approximate area of the trapezium is 81.6 sq. cm.
Answer: Option (b) 81.6 sq. cm.
Given:
Parallel sides of trapezium = 22 cm, 12 cm
Other sides of trapezium = 8 cm, 6 cm
To find: Approximate area of trapezium
Formula for area of trapezium:
Area = 1/2 × (sum of parallel sides) × (distance between parallel sides)
Steps to solve:
1. Find the distance between parallel sides:
We can use Pythagoras theorem to find the distance between parallel sides.
a² = b² + c²
where a = difference between parallel sides, b and c = lengths of other sides
Substituting the given values, we get:
a² = 8² - 6²
a² = 64 - 36
a² = 28
a ≈ 5.29 cm
Therefore, the distance between parallel sides is approximately 5.29 cm.
2. Substitute the values in the formula for area:
Area = 1/2 × (22 + 12) × (5.29)
Area = 1/2 × 34 × 5.29
Area ≈ 81.6 sq. cm
Therefore, the approximate area of the trapezium is 81.6 sq. cm.
Answer: Option (b) 81.6 sq. cm.
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Find the approximate area of a trapezium whose parallel sides are 22 cm, 12 cm and the other sides are 8 cm and 6 cm.a)73.3 sq. cm.b)81.6 sq. cm.c)31.3 sq. cm.d)75.5 sq. cm.Correct answer is option 'B'. Can you explain this answer?
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Find the approximate area of a trapezium whose parallel sides are 22 cm, 12 cm and the other sides are 8 cm and 6 cm.a)73.3 sq. cm.b)81.6 sq. cm.c)31.3 sq. cm.d)75.5 sq. cm.Correct answer is option 'B'. Can you explain this answer? for SSC 2024 is part of SSC preparation. The Question and answers have been prepared according to the SSC exam syllabus. Information about Find the approximate area of a trapezium whose parallel sides are 22 cm, 12 cm and the other sides are 8 cm and 6 cm.a)73.3 sq. cm.b)81.6 sq. cm.c)31.3 sq. cm.d)75.5 sq. cm.Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for SSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the approximate area of a trapezium whose parallel sides are 22 cm, 12 cm and the other sides are 8 cm and 6 cm.a)73.3 sq. cm.b)81.6 sq. cm.c)31.3 sq. cm.d)75.5 sq. cm.Correct answer is option 'B'. Can you explain this answer?.
Find the approximate area of a trapezium whose parallel sides are 22 cm, 12 cm and the other sides are 8 cm and 6 cm.a)73.3 sq. cm.b)81.6 sq. cm.c)31.3 sq. cm.d)75.5 sq. cm.Correct answer is option 'B'. Can you explain this answer? for SSC 2024 is part of SSC preparation. The Question and answers have been prepared according to the SSC exam syllabus. Information about Find the approximate area of a trapezium whose parallel sides are 22 cm, 12 cm and the other sides are 8 cm and 6 cm.a)73.3 sq. cm.b)81.6 sq. cm.c)31.3 sq. cm.d)75.5 sq. cm.Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for SSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the approximate area of a trapezium whose parallel sides are 22 cm, 12 cm and the other sides are 8 cm and 6 cm.a)73.3 sq. cm.b)81.6 sq. cm.c)31.3 sq. cm.d)75.5 sq. cm.Correct answer is option 'B'. Can you explain this answer?.
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