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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 m^{2}

`"Area of ΔBEC "=1/2xxCExxBF`

`rArr84=1/2xx15xxBF`

`rArrBF=168/15=11.2 m`

Area of ABED = BF × DE = 11.2 × 10 = 112 m^{2}

Area of the field = 84 + 112 = 196 m^{2}

Concept: Application of Heron’s Formula in Finding Areas of Quadrilaterals

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