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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.
Answer :

Here, ABCD is a trapezium and AB || DC.

Here, ABCD is a trapezium and CE || DA and CF?AB.

image

Now, AB = 25 m, BC = 14 m, CD = 10 m, DA = 13 m, AE = 10 m and CE = 13m
? EB = 25 - 10 = 15 m

Now, for ?EBC, we have,
s=a+b+c2
? s=15+14+132=422=21m

Now, Area of triangle
= 21(21?15)(21?14)(21?13)
(Since, Heron's formula [area = s(s?a)(s?b)(s?c)])
= 21×6×7×8

= 7×3×3×2×7×4×2
= 7×3×4m2
= 84cm2

Also, Area of triangle ?EBC
= frac12 × Base × Height
= 12 × 15 × CF
? frac12 × 15 × CF = 84
? CF = 84×215=16815=11.2m

Now, area of the trapezium ABCD
= 12 × (Sum of parallel sides) × (Distance between parallel sides)
= 12 × (AB + CD) × CF
= 12 × (25 + 10) × 11.2
= 12 × 35 × 11.2
= 35 × 5.65

Therefore, the area of the field is 196 m2.