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.
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Solution
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