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