Question

find the area of a trapezium whose parallel sides are 11m and 25m long, and the nonparallel sides are 15m and 13m long

Answer 1

Let ABCD be the trapezium, such that AD = 11 m, BC = 25 m, AB = 13 m and CD = 15 m.

Draw AM perpendicular from A on to BC. Let BM = x.

Draw DN perpendicular from D on to BC. Let NC = 14-x.

Let AM = DN = h.

In RAT, ABM, 13^2 = h^2+x^2 …(1)

In RAT, DCN, 15^2 = h^2+(14-x)^2 …(2)

Subtract (1) from (2)

15^2–13^2 = 56 = 196–28x, or

140 = 28x, or x = 5

From (1), 13^2 = 169 = h^2+25, or

h^2 = 144, or h = 12 m

Area of ABCD = (11+15)*12/2 = 26*6 = 156 sq m.

Answer : 156 sq m.
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