A field is in the shape of a trapezium whose parallel sides are 25m and 10m. If its non-parallel sides are 14m and 13m, find its area.

Explanation

Let ABCD be the field in the form of a trapezium in which AB||CD such that AB = 25 m, BC = 13 m, CD = 10 m and DA = 14 m.
Draw CE||Da and CF `bot` EB.

Clearly, ADCE is a parallelogram.
`therefore" "CE = DA = 14 m and AE = CD = 10 m`.
`therefore" "EB = AB - AE = (25 - 10)m = 15 m`.
In `Delta`EBC, we have
EB = 15 m, BC = 13 m and CE = 14 m.
`therefore" "a = 15 m, b = 13 m and c = 14 m`.
`therefore" "s=(1)/(2)(15 + 13 + 14)m = 21 m`.
`therefore" "(s-a)=(21-15)m = 6m, (s-b)=(21-13)m = 8m and (s-c) = (21 - 14)m = 7 m`.
`therefore" ""area"(Delta EBC)=sqrt(s(s-a)(s-b)(s-c))=sqrt(21 xx 6 xx 8 xx 7)m^(2)`
`=sqrt(7 xx 3 xx 3 xx 2 xx 2 xx 4 xx 7)m^(2)`
`=(7 xx 3 xx 2 xx 2)m^(2)=84 m^(2)`.
Also, area `(Delta EBC)=((1)/(2)xx EB xx CF)=((1)/(2) xx 15 m xx CF)`
`therefore" "(1)/(2)xx 15 m xx CF = 84 m^(2) rArr CF = (84 xx 2)/(15)m = (56)/(5)m = 11.2 m`.
`therefore" "CF = 11.2 m`.
Area (trap. ABCD)`=(1)/(2)xx(AB + CD)xxCF`
`={(1)/(2)xx(25 + 10)xx 11.2}m^(2)`
`=(35 xx 5.6)m^(2) = 196 m^(2)`.
Hence, the area of the trapezium ABCD is 196 `m^(2)`.