a filed is in the shape of a trapezium. The parallel sides are 10m and 25m the non parallel sides are 14m and 13m. Find the area of the field. [ch: heron's formula]
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GivEn:
- Parallel sides of a trapezium shaped field are 10 m and 25 m.
- Non - parallel sides of a trapezium shaped field are 14 m and 13 m.
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To find:
- Area of the field.
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SoluTion:
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ABCD is a trapezium.
⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀
Now, Construct a line CE which is parallel to AD.
⠀⠀⠀⠀⠀⠀⠀
Therefore,
- CE = AD = 13 m
- AE = CD = 10 m
- EB = AB - AE = (25 m - 10 m) = 15 m
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⠀⠀⠀⠀⠀⠀⠀
we have,
- EC = 13 m
- BC = 14 m
- EB = 15 m
⠀⠀⠀⠀⠀⠀⠀
Now, Using Heron's Formula,
⠀⠀⠀⠀⠀⠀⠀
we have to find area of ∆ EBC -
⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀
where,
⠀⠀⠀⠀⠀⠀⠀
s = semi - perimeter
⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀
━━━━━━━━━━━━━━━
Now,
⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀
Again, Area of ∆ EBC
using base and height,
⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀
━━━━━━━━━━━━━━━
⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀
As we know that,
⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀
Hence, Area of trapezium shaped field is 196 m².
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