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The perimeter of of a trapezium is 104m, its non-parallel sides are 18m and 22m and its altitude is 16m. Find its area?
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The perimeter of of a trapezium is 104m, its non-parallel sides are 18...
Perimeter of the Trapezium:
The perimeter of a trapezium is the sum of the lengths of all its sides. In this case, the perimeter is given as 104m. Let's denote the lengths of the non-parallel sides as a and b, where a = 18m and b = 22m.
Therefore, the perimeter of the trapezium can be expressed as:
Perimeter = a + b + c + d
Given that the altitude (height) of the trapezium is 16m, we can calculate the lengths of the parallel sides by using the Pythagorean theorem. The parallel sides are represented by c and d.
Calculating the Lengths of the Parallel Sides:
Using the Pythagorean theorem, we can calculate the lengths of the parallel sides as follows:
c^2 = (a - b)^2 + h^2
c^2 = (18 - 22)^2 + 16^2
c^2 = (-4)^2 + 16^2
c^2 = 16 + 256
c^2 = 272
c = √272
c ≈ 16.49m
d^2 = (a + b)^2 + h^2
d^2 = (18 + 22)^2 + 16^2
d^2 = 40^2 + 16^2
d^2 = 1600 + 256
d^2 = 1856
d = √1856
d ≈ 43.07m
Calculating the Area of the Trapezium:
The area of a trapezium can be calculated using the formula:
Area = (a + b) * h / 2
Substituting the given values, we have:
Area = (18 + 22) * 16 / 2
Area = 40 * 16 / 2
Area = 640 / 2
Area = 320m^2
Therefore, the area of the trapezium is 320 square meters.
The perimeter of a trapezium is the sum of the lengths of all its sides. In this case, the perimeter is given as 104m. Let's denote the lengths of the non-parallel sides as a and b, where a = 18m and b = 22m.
Therefore, the perimeter of the trapezium can be expressed as:
Perimeter = a + b + c + d
Given that the altitude (height) of the trapezium is 16m, we can calculate the lengths of the parallel sides by using the Pythagorean theorem. The parallel sides are represented by c and d.
Calculating the Lengths of the Parallel Sides:
Using the Pythagorean theorem, we can calculate the lengths of the parallel sides as follows:
c^2 = (a - b)^2 + h^2
c^2 = (18 - 22)^2 + 16^2
c^2 = (-4)^2 + 16^2
c^2 = 16 + 256
c^2 = 272
c = √272
c ≈ 16.49m
d^2 = (a + b)^2 + h^2
d^2 = (18 + 22)^2 + 16^2
d^2 = 40^2 + 16^2
d^2 = 1600 + 256
d^2 = 1856
d = √1856
d ≈ 43.07m
Calculating the Area of the Trapezium:
The area of a trapezium can be calculated using the formula:
Area = (a + b) * h / 2
Substituting the given values, we have:
Area = (18 + 22) * 16 / 2
Area = 40 * 16 / 2
Area = 640 / 2
Area = 320m^2
Therefore, the area of the trapezium is 320 square meters.
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The perimeter of of a trapezium is 104m, its non-parallel sides are 18m and 22m and its altitude is 16m. Find its area?
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The perimeter of of a trapezium is 104m, its non-parallel sides are 18m and 22m and its altitude is 16m. Find its area? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about The perimeter of of a trapezium is 104m, its non-parallel sides are 18m and 22m and its altitude is 16m. Find its area? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The perimeter of of a trapezium is 104m, its non-parallel sides are 18m and 22m and its altitude is 16m. Find its area?.
The perimeter of of a trapezium is 104m, its non-parallel sides are 18m and 22m and its altitude is 16m. Find its area? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about The perimeter of of a trapezium is 104m, its non-parallel sides are 18m and 22m and its altitude is 16m. Find its area? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The perimeter of of a trapezium is 104m, its non-parallel sides are 18m and 22m and its altitude is 16m. Find its area?.
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