If the length of three sides of a trapezium other than the base is 10 cm each, find the area of the trapezium, when it is maximum.

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