The parallel side of a trepezium are 20cm ans 10cm its non parallel sidea are both equal and each being 15 cm. find the area of trepezium
Answers
Given:
✰ The parallel side of a trepezium are 20 cm and 10 cm respectively.
✰ Its non parallel sides are both equal and each being 15 cm.
To find:
✠ The area of trepezium.
Solution:
In the diagram it is clear that 2 are triangles and one is rectangle.
To calculate the area of trapezium, we first need to find the height of the trapezium.
In ∆ACD,
By using Pythagoras theorem,
⤳ AC² = AD² + CD²
⤳ 15² = AD² + 5²
⤳ 225 = AD² + 25
⤳ AD² = 225 - 25
⤳ AD² = 200
⤳ AD = √200 cm
∴ The height of the trapezium = √200 cm
Now, finally find the area of trapezium by using formula. Putting the values in the formula and then doing the required calculations.
✭ Area of a trapezium = 1/2 × (a + b) × h ✭
Where,
- a and b are the parallel sides of the trapezium.
- h is the height that means the distance between its parallel sides.
Putting the values in the formula, we have:
➤ Area of a trapezium = 1/2 × (20 + 10) × √200
➤ Area of a trapezium = 1/2 × 30 × √200
➤ Area of a trapezium = 15 × √200
➤ Area of a trapezium ≈ 212.132 cm²
∴ The area of trepezium ≈ 212.132 cm²
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