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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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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, By Heron’s formula, Area of triangle Area of ΔBEC m2= 84 m2 Area of ΔBEC ⇒...
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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, 

By Heron’s formula,

Area of triangle

Area of ΔBEC 

m2= 84 m2

Area of ΔBEC 

 84 = 12 × 15 × BF BF = 16815 = 11.2 m⇒ 84 = 12 × 15 × BF⇒ BF = 16815 = 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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196 is the area of a trapezium.
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