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The parallel sides of a trapezium are 20 cm and 10 cm. Its nonparallel sides are both equal, each being 13 cm. Find the area of the trapezium.?
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The parallel sides of a trapezium are 20 cm and 10 cm. Its nonparallel...
Given Data
- Parallel sides (bases): a = 20 cm, b = 10 cm
- Non-parallel sides (legs): c = 13 cm (both sides equal)
Step 1: Calculate the height of the trapezium
To find the area of the trapezium, we first need to calculate its height. We can drop perpendiculars from the endpoints of the shorter base (10 cm) to the longer base (20 cm), creating two right triangles.
- Let’s denote:
- Height = h
- The distance from the endpoint of the shorter base to one of the perpendiculars = x
Using the Pythagorean theorem in one of the right triangles:
- (13 cm)^2 = h^2 + x^2
We also know the total length of the longer base minus the shorter base:
- 20 cm - 10 cm = 10 cm
Since there are two right triangles, we have:
- 2x = 10 cm
- Thus, x = 5 cm
Now we can substitute x back into the Pythagorean theorem:
- 13^2 = h^2 + 5^2
- 169 = h^2 + 25
- h^2 = 144
- h = 12 cm
Step 2: Calculate the Area of the Trapezium
The area (A) of a trapezium can be calculated using the formula:
- A = (1/2) * (a + b) * h
Substituting the values we have:
- A = (1/2) * (20 + 10) * 12
- A = (1/2) * 30 * 12
- A = 15 * 12
- A = 180 cm²
Conclusion
The area of the trapezium is 180 cm².
- Parallel sides (bases): a = 20 cm, b = 10 cm
- Non-parallel sides (legs): c = 13 cm (both sides equal)
Step 1: Calculate the height of the trapezium
To find the area of the trapezium, we first need to calculate its height. We can drop perpendiculars from the endpoints of the shorter base (10 cm) to the longer base (20 cm), creating two right triangles.
- Let’s denote:
- Height = h
- The distance from the endpoint of the shorter base to one of the perpendiculars = x
Using the Pythagorean theorem in one of the right triangles:
- (13 cm)^2 = h^2 + x^2
We also know the total length of the longer base minus the shorter base:
- 20 cm - 10 cm = 10 cm
Since there are two right triangles, we have:
- 2x = 10 cm
- Thus, x = 5 cm
Now we can substitute x back into the Pythagorean theorem:
- 13^2 = h^2 + 5^2
- 169 = h^2 + 25
- h^2 = 144
- h = 12 cm
Step 2: Calculate the Area of the Trapezium
The area (A) of a trapezium can be calculated using the formula:
- A = (1/2) * (a + b) * h
Substituting the values we have:
- A = (1/2) * (20 + 10) * 12
- A = (1/2) * 30 * 12
- A = 15 * 12
- A = 180 cm²
Conclusion
The area of the trapezium is 180 cm².
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The parallel sides of a trapezium are 20 cm and 10 cm. Its nonparallel sides are both equal, each being 13 cm. Find the area of the trapezium.?
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The parallel sides of a trapezium are 20 cm and 10 cm. Its nonparallel sides are both equal, each being 13 cm. Find the area of the trapezium.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The parallel sides of a trapezium are 20 cm and 10 cm. Its nonparallel sides are both equal, each being 13 cm. Find the area of the trapezium.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The parallel sides of a trapezium are 20 cm and 10 cm. Its nonparallel sides are both equal, each being 13 cm. Find the area of the trapezium.?.
The parallel sides of a trapezium are 20 cm and 10 cm. Its nonparallel sides are both equal, each being 13 cm. Find the area of the trapezium.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The parallel sides of a trapezium are 20 cm and 10 cm. Its nonparallel sides are both equal, each being 13 cm. Find the area of the trapezium.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The parallel sides of a trapezium are 20 cm and 10 cm. Its nonparallel sides are both equal, each being 13 cm. Find the area of the trapezium.?.
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