Answer :

Given, A trapezium is given, and the length of three sides is 10cm.

To Find: Find the area of a trapezium,


Explanation: Let Assume, ABCD is a trapezium



Now, Make a construction DP perpendicular AB and CQ perpendicular AB


So, ∆ADP≡∆BQC


Now, Let AP = x cm , then BQ = x cm


So,




Area of trapezium ABCD =


Area of ABCD




For the maximum area, we know




x2 + 5x - 50 = 0


x2 + 10x - 5x - 50 = 0


x(x + 10) - 5(x + 10) = 0


(x + 10)(x - 5) = 0


X = 5, - 10


We will neglect negative values


Now,


(






Now, Area at x = 5






Area of the trapezium is maximum when x = 5


A = (10 + 5)


cm2


Hence, The Area of the trapezium is


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