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A field is in the shape of trapezium whose parallel sides are 65 m and 40 m and non parallel sides are 56 m and 36m.Find the area of the field.?
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A field is in the shape of trapezium whose parallel sides are 65 m and...
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A field is in the shape of trapezium whose parallel sides are 65 m and...
Given information:
- The parallel sides of the trapezium are 65 m and 40 m.
- The non-parallel sides of the trapezium are 56 m and 36 m.
Approach:
To find the area of the trapezium, we can use the formula:
Area = (1/2) × (a + b) × h
Where:
- a and b are the lengths of the parallel sides of the trapezium
- h is the perpendicular distance between the parallel sides
We can find the value of h using the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Solution:
Step 1: Find the value of h using the Pythagorean theorem:
- Let's consider the sides 65 m and 56 m as the two legs of a right-angled triangle.
- Let h be the perpendicular distance between the parallel sides.
Using the Pythagorean theorem:
h^2 = 65^2 - 56^2
h^2 = 4225 - 3136
h^2 = 1089
h = √1089
h = 33 m
Step 2: Substitute the values of a, b, and h into the formula for the area of the trapezium:
Area = (1/2) × (65 + 40) × 33
Calculating the value:
Area = (1/2) × 105 × 33
Area = 52.5 × 33
Area = 1732.5 square meters
Answer:
The area of the trapezium is 1732.5 square meters.
- The parallel sides of the trapezium are 65 m and 40 m.
- The non-parallel sides of the trapezium are 56 m and 36 m.
Approach:
To find the area of the trapezium, we can use the formula:
Area = (1/2) × (a + b) × h
Where:
- a and b are the lengths of the parallel sides of the trapezium
- h is the perpendicular distance between the parallel sides
We can find the value of h using the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Solution:
Step 1: Find the value of h using the Pythagorean theorem:
- Let's consider the sides 65 m and 56 m as the two legs of a right-angled triangle.
- Let h be the perpendicular distance between the parallel sides.
Using the Pythagorean theorem:
h^2 = 65^2 - 56^2
h^2 = 4225 - 3136
h^2 = 1089
h = √1089
h = 33 m
Step 2: Substitute the values of a, b, and h into the formula for the area of the trapezium:
Area = (1/2) × (65 + 40) × 33
Calculating the value:
Area = (1/2) × 105 × 33
Area = 52.5 × 33
Area = 1732.5 square meters
Answer:
The area of the trapezium is 1732.5 square meters.
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A field is in the shape of trapezium whose parallel sides are 65 m and 40 m and non parallel sides are 56 m and 36m.Find the area of the field.?
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A field is in the shape of trapezium whose parallel sides are 65 m and 40 m and non parallel sides are 56 m and 36m.Find the area of the field.? 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 A field is in the shape of trapezium whose parallel sides are 65 m and 40 m and non parallel sides are 56 m and 36m.Find the area of the field.? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A field is in the shape of trapezium whose parallel sides are 65 m and 40 m and non parallel sides are 56 m and 36m.Find the area of the field.?.
A field is in the shape of trapezium whose parallel sides are 65 m and 40 m and non parallel sides are 56 m and 36m.Find the area of the field.? 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 A field is in the shape of trapezium whose parallel sides are 65 m and 40 m and non parallel sides are 56 m and 36m.Find the area of the field.? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A field is in the shape of trapezium whose parallel sides are 65 m and 40 m and non parallel sides are 56 m and 36m.Find the area of the field.?.
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