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The parallel sides of a trapezium are 10 cm and 22 cm. Its non-parallel sides are 10 cm each then the area of the trapezium is
- a)56 cm2
- b)128 cm2
- c)64 cm2
- d)None of the abov
Correct answer is option 'B'. Can you explain this answer?
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The parallel sides of a trapezium are 10 cm and 22 cm. Its non-paralle...
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The parallel sides of a trapezium are 10 cm and 22 cm. Its non-paralle...
Given:
- Parallel sides of the trapezium: 10 cm and 22 cm
- Non-parallel sides of the trapezium: 10 cm each
To find:
- Area of the trapezium
Explanation:
A trapezium is a quadrilateral with one pair of parallel sides. To find the area of a trapezium, we can use the formula:
Area = (1/2) × (sum of parallel sides) × (height)
Step 1: Finding the height of the trapezium
- Since the non-parallel sides are equal in length, the height of the trapezium is the perpendicular distance between the parallel sides.
- We can use the Pythagorean theorem to find the height.
- Let the height be 'h'.
- According to the Pythagorean theorem, in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
- So, we have: (h^2) + (10^2) = (22^2)
- Simplifying the equation, we get: h^2 + 100 = 484
- h^2 = 484 - 100
- h^2 = 384
- h = √384
- h = 19.6 cm (approx.)
Step 2: Finding the area of the trapezium
- Now that we have the height, we can substitute the values into the formula for the area of a trapezium.
- Area = (1/2) × (sum of parallel sides) × (height)
- Area = (1/2) × (10 + 22) × 19.6
- Area = (1/2) × 32 × 19.6
- Area = 16 × 19.6
- Area = 313.6 cm^2
Conclusion:
The area of the trapezium is 313.6 cm^2, which is not among the given answer options. Therefore, the correct answer is none of the above.
- Parallel sides of the trapezium: 10 cm and 22 cm
- Non-parallel sides of the trapezium: 10 cm each
To find:
- Area of the trapezium
Explanation:
A trapezium is a quadrilateral with one pair of parallel sides. To find the area of a trapezium, we can use the formula:
Area = (1/2) × (sum of parallel sides) × (height)
Step 1: Finding the height of the trapezium
- Since the non-parallel sides are equal in length, the height of the trapezium is the perpendicular distance between the parallel sides.
- We can use the Pythagorean theorem to find the height.
- Let the height be 'h'.
- According to the Pythagorean theorem, in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
- So, we have: (h^2) + (10^2) = (22^2)
- Simplifying the equation, we get: h^2 + 100 = 484
- h^2 = 484 - 100
- h^2 = 384
- h = √384
- h = 19.6 cm (approx.)
Step 2: Finding the area of the trapezium
- Now that we have the height, we can substitute the values into the formula for the area of a trapezium.
- Area = (1/2) × (sum of parallel sides) × (height)
- Area = (1/2) × (10 + 22) × 19.6
- Area = (1/2) × 32 × 19.6
- Area = 16 × 19.6
- Area = 313.6 cm^2
Conclusion:
The area of the trapezium is 313.6 cm^2, which is not among the given answer options. Therefore, the correct answer is none of the above.
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The parallel sides of a trapezium are 10 cm and 22 cm. Its non-parallel sides are 10 cm each then the area of the trapezium isa)56 cm2b)128cm2c)64cm2d)None of the abovCorrect answer is option 'B'. Can you explain this answer?
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