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Question
A field is in the shape of a trapezium whose parallel sides are 25 m and 10 m. The non-parallel sides are 14 m and 13 m. Find the area of the field.
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Solution
Draw a line BE parallel to AD and draw a perpendicular BF on CD.
It can be observed that ABED is a parallelogram.
BE = AD = 13 m
ED = AB = 10 m
EC = 25 − ED = 15 m
For ΔBEC,
Semi-perimeter,
`s=(13+14+15)/2=21 m`
By Heron’s formula,
`"Area of triangle "=sqrt(s(s-a)(s-b)(s-c))`
`"Area of ΔBEC "=[sqrt(21(21-13)(21-14)(21-15))]m^2`
`=[sqrt(21(8)(7)(6))]m^2`
= 84 m2
`"Area of ΔBEC "=1/2xxCExxBF`
`rArr84=1/2xx15xxBF`
`rArrBF=168/15=11.2 m`
Area of ABED = BF × DE = 11.2 × 10 = 112 m2
Area of the field = 84 + 112 = 196 m2
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