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The area of trapezium with the equal non parallel sides is 168cm2 if the lengths of the parallel sides are 36m and 20 m find the length of the non parallel sides?
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The area of trapezium with the equal non parallel sides is 168cm2 if t...
Given Information
- Area of the trapezium (A) = 168 cm²
- Length of the parallel sides (a) = 36 m
- Length of the parallel side (b) = 20 m
Conversion of Units
- Convert area to square meters:
- 1 cm² = 0.0001 m²
- 168 cm² = 168 × 0.0001 = 0.0168 m²
Area Formula for Trapezium
- The area of a trapezium is given by:
A = (1/2) × (a + b) × h
- Where:
- A = Area
- a = Length of the first parallel side
- b = Length of the second parallel side
- h = Height of the trapezium
Calculating the Height
- Rearranging the area formula:
h = (2A) / (a + b)
- Substitute the values:
h = (2 × 0.0168) / (36 + 20)
h = 0.0336 / 56
h = 0.0006 m
Finding the Length of Non-Parallel Sides
- Let the length of the non-parallel sides (c) be equal.
- Use the Pythagorean theorem:
c² = (h²) + ((a - b)/2)²
- Substitute values:
c² = (0.0006)² + ((36 - 20)/2)²
c² = 0.00000036 + 8²
c² = 0.00000036 + 64
- Therefore, c = √64.00000036 ≈ 8 m
Final Answer
- The length of each non-parallel side is approximately 8 m.
- Area of the trapezium (A) = 168 cm²
- Length of the parallel sides (a) = 36 m
- Length of the parallel side (b) = 20 m
Conversion of Units
- Convert area to square meters:
- 1 cm² = 0.0001 m²
- 168 cm² = 168 × 0.0001 = 0.0168 m²
Area Formula for Trapezium
- The area of a trapezium is given by:
A = (1/2) × (a + b) × h
- Where:
- A = Area
- a = Length of the first parallel side
- b = Length of the second parallel side
- h = Height of the trapezium
Calculating the Height
- Rearranging the area formula:
h = (2A) / (a + b)
- Substitute the values:
h = (2 × 0.0168) / (36 + 20)
h = 0.0336 / 56
h = 0.0006 m
Finding the Length of Non-Parallel Sides
- Let the length of the non-parallel sides (c) be equal.
- Use the Pythagorean theorem:
c² = (h²) + ((a - b)/2)²
- Substitute values:
c² = (0.0006)² + ((36 - 20)/2)²
c² = 0.00000036 + 8²
c² = 0.00000036 + 64
- Therefore, c = √64.00000036 ≈ 8 m
Final Answer
- The length of each non-parallel side is approximately 8 m.
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The area of trapezium with the equal non parallel sides is 168cm2 if the lengths of the parallel sides are 36m and 20 m find the length of the non parallel sides?
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The area of trapezium with the equal non parallel sides is 168cm2 if the lengths of the parallel sides are 36m and 20 m find the length of the non parallel sides? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The area of trapezium with the equal non parallel sides is 168cm2 if the lengths of the parallel sides are 36m and 20 m find the length of the non parallel sides? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The area of trapezium with the equal non parallel sides is 168cm2 if the lengths of the parallel sides are 36m and 20 m find the length of the non parallel sides?.
The area of trapezium with the equal non parallel sides is 168cm2 if the lengths of the parallel sides are 36m and 20 m find the length of the non parallel sides? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The area of trapezium with the equal non parallel sides is 168cm2 if the lengths of the parallel sides are 36m and 20 m find the length of the non parallel sides? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The area of trapezium with the equal non parallel sides is 168cm2 if the lengths of the parallel sides are 36m and 20 m find the length of the non parallel sides?.
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