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Question

The parallel sides of a trapezium are 25 cm and 13 cm; its nonparallel sides are equal, each being 10 cm, find the area of the trapezium.

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Solution

Given:The parallel sides of a trapezium are 25 cm and 13 cm. Its nonparallel sides are equal in length and each is equal to 10 cm.A rough sketch for the given trapezium is given below:


In above figure, we observe that both the right angle trangles AMD and BNC are congruent triangles.AD = BC = 10 cmD= CN = x cmDMA =CNB = 90°Hence, the third side of both the triangles will also be equal. AM=BNAlso, MN=13Since AB = AM+MN+NB: 25=AM+13+BNAM+BN=25-13=12 cmOr, BN+BN=12 cm (Because AM=BN)2 BN=12BN=122=6 cm AM = BN = 6 cm.Now, to find the value of x, we will use the Pythagoras theorem in the right angle triangle AMD, whose sides are 10, 6 and x.(Hypotenuse)2=(Base)2+(Altitude)2(10)2=(6)2+(x)2100=36+x2x2=100-36=64x=64=8 cmDistance between the parallel sides = 8 cm Area of trapezium = 12×(Sum of parallel sides)×(Distance between parallel sides)=12×(25+13)×(8)=152 cm2

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