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Question

Find the area of Fig. 20.35 as the sum of the areas of two trapezium and a rectangle.

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Solution

The given figure is:



In the given figure, we have a rectangle of length 50 cm and width 10 cm, and two similar trapeziums with parallel sides as 30 cm and 10 cm at both ends.Suppose x is the perpendicular distance between the parallel sides in both the trapeziums.We have:Total length of the given figure= Length of the rectangle+ 2×Perpendicular distance between the parallel sides in both the trapeziums70=50+2×x2×x=70-50=20x=202=10 cmNow, area of the complete figure=(area of the rectangle with sides 50 cm and 10 cm)+2×(area of the trapezium with parallel sides 30 cm and 10 cm, and height 10 cm)=(50×10)+2×[12×(30+10)×(10)]=500+2×[200]=900 cm2

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