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Question

Find the area of pentagon ABCDE, given that EB = 10 cm, DC = 5 cm, AF = 3 cm and DG = 4 cm.


A
15 cm2
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B
30 cm2
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C
45 cm2
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D
60 cm2
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Solution

The correct option is C 45 cm2
Given,
EB = 10 cm,
DC = 5 cm
AF = 3 cm and
DG = 4 cm.

Area of pentagon ABCDE
= Area of trapezium BCDE + Area of AEB

Area of trapezium BCDE
=12×(Sum of parallel sides)×height
=12×(CD+BE)×DG
=12×(5+10)×4
=12×(15)×4
= 15×2
= 30 cm2

Area of AEB
=12×base×height
=12×BE×AF
=12×10×3=15 cm2

Area of pentagon ABCDE
= Area of trapezium BCDE + Area of AEB
= 30 cm2 + 15 cm2
= 45 cm2

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