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Question

Find the area of given figure, if AB = EF = 12 cm, CD = 10 cm and PQ = QR = 5 cm.


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Solution

PQ is perpendicular to AB and CD.
AB || CD
ABCD is a trapezium

Similarly,
QR is perpendicular to CD and EF.
CD || EF
CDEF is a trapezium

Therefore,
Area of given figure
= Area of trapezium ABDC + Area of trapezium CDFE

We know that
Area of trapezium
=12×(Sum of parallel sides)×height

Area of trapezium ABDC
=12×(AB+CD)×PQ
=12×(12+10)×5=12×22×5
= 11×5
= 55 cm2

Area of trapezium CDFE
=12×(EF+CD)×QR
=12×(12+10)×5=12×22×5
= 11×5
= 55 cm2

Therefore, Area of given figure = 55 + 55 = 110 cm2

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