A trapezium has a pair of parallel sides of different lengths so in order to find its 2nd parallel side the information given must include its height.
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Trapezium :Area(A) = 1/2 h(a + b)where a and b are the length of the parallel sidesh= distance between two parallel lines .Perimeter(P) = a + b + c + dwhere a,b,c and d are the length of the sides.
The area of a trapezium is given by 0.5*(a+b)*h where a and b are the lengths of the parallel sides and h is the vertical distance between them. The fact that the trapezium is isosceles does not matter. A trapezium is a 2 dimensional object and so it has no volume.
In UK terms:- Area = 0.5*(sum of parallel sides)*height and measured in square units
Area of trapezium = 0.5(sum of parallel sides)*heightSo, 180 = 0.5*(sum of parallel sides)*9So Sum of parallel sides = 40 cm.If the smaller parallel side is x cm, then the larger side is x+6 cm and their sum is 40 cmso x + x+6 = 40 or 2x = 34 or x = 17 and x+6 = 23.The two parallel sides are 17 and 23 cm.
Area of a trapezoid = 0.5*(sum of parallel sides)*height