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Question

Find the area of the field ABCDEFG shown in the figure, if GI, JC, FH, and GE are 1 cm, 2 cm, 4 cm, and 5 cm respectively.

A
20 cm2
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B
21 cm2
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C
40 cm2
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D
41 cm2
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Solution

The correct option is D 41 cm2
Field can be divided into four simple figures ,
Trapezium ABDE, BCD, AGE and
GFE
Hence Area of field =
Area of trapezium ABDE + Area of BCD + Area of AGE + Area of GFE
For the trapezium ABDE
AB = 4 cm , ED = 3cm ,AE = height = 6 cm
Area of trapezium
= 12×(sum of parallel sides)×height
= 12×(AB+DE)×AE
= 12×(4+3)×6
= 12×7×6 =7×62 = 3×7 = 21 cm2

Area of triangle = 12×base×height

For BCD ; base = 7 cm and height = 2 cm
Area of BCD = 12×BD×CJ = 12×7×2
Area of BCD = 7 cm2

For AGE ; base = 6 cm and height = 1 cm

Area of AGE = 12×AE×GI = 12×6×1
Area of AGE = 3 cm2

For GFE ; base = 5 cm and height = 4 cm
Area of GFE = 12×GE×FH = 12×5×4
Area of GFE = 10 cm2

Area of field = 21+7+10+3 = 41 cm2

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