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in Perimeter and Area of Plane Figures by (29.9k points)
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Find the area of a trapezium whose parallel sides are 11 cm and 25 cm long and nonparallel sides are 15 cm and 13 cm.

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We will divide the trapezium into a triangle and a parallelogram

Difference in the lengths of parallel sides = 25 - 11 = 14 cm

We can represent this in the following figure:

Trapezium ABCD is divide into parallelogram AECD and triangle CEB.

Consider triangle CEB.

In triangle CEB, we have,

EB = 25 - 11 = 14 cm

Using Hero’s theorem, we will first evaluate the semi-perimeter of triangle CEB and then evaluate its area

= 84  cm2

Also,

Area of parallelogram AECD = Height x Base = 12 x 11 = 132 cm2

Area of trapezium ABCD = Ar \((\triangle BEC)\) + Ar(parallelogram AECD) = 132 + 84 = 216 cm2

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