Let

'a' and 'b' be the parallel sides of the trapezium
h = 12 m the height of the trapezium
Area = (a + b)*h/2

The Area of a trapezium is 216 m^2

(a + b)*h/2 = 216

(a + b)12/2 = 216

(a + b)6 = 216

One of the parallel sides is 14 m less than the other means:

a = b + 14

By solving the system of equations

a = b + 14
(a + b)6 = 216

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to see the step by step solution of the system click here
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a = 25 m

b = 11 m

The lengths of the parallel sides of the trapezium are 25 m and 11 m.