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kíndlч ѕσlvє thíѕ quєѕtíσn αѕ fαѕt αѕ pσѕѕíвlє
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Given :------
- Parallel sides of Trapezium are 25 and 10 .
- Non parallel sides are 14 and 13..
To Find :---
- Area of Trapezium ?
Construction :-----
- Draw a line From Side 10cm to side 25cm, so that, it will make a parallelogram of opposite sides 10cm and 13cm each ..
- once we make this trapezium become = parallelogram + ∆ with sides 13, 14 and (25-10) = 15cm.
Formula used :------
- Area of ∆ by Heron Formula = √s(s-a)(s-b)(s-c)
- Area of ∆ = 1/2 * Base * Height
- Area of Trapezium = 1/2*(sum of ll sides) * Height .
______________________________________
First we will find Area of ∆ with sides 13,14 and 15,
→ semi-perimeter = (13+14+15)/2 = 42/2 = 21cm
→ Area ∆ = √21(21-13)(21-14)(21-15)
→ Area ∆ = √21*7*8*6
→ Area ∆ = 84cm²
So, Height of ∆ with base 15cm now,
→ 1/2 * 15 * Height = 84
→ Height = (168/15)cm
______________________________________
So,
Area of Trapezium = 1/2*(10+25) * (168/15) = 1/2*35* 168/15
→ Area = 196cm²
________________________________
Hence, Area of Trapezium will be 196cm² ....
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