Question

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Find the area of Pentagon CHINA, if CN=12 cm, CJ=10 cm, CB=8 cm, CG=7 cm,HG=7 cm, IJ=9 cm and AB=5 cm.

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Answer 1

now add all the areas you will get the answer

Answer 2

Area of Pentagon CHINA = 87.5 cm²

Step-by-step explanation:

Area of CHINA

= Area of Δ CGH  + Area of Trapezium HGJI  + Area of Δ IJN  + Area of ΔCAN

Area of Δ CGH  = (1/2) CG * GH  = (1/2) * 7 * 7  = 24.5  cm²

Area of Trapezium HGJI  = (1/2) (HG + IJ) * GJ

GJ = CJ - CG = 10 - 7 = 3

= (1/2) (7 + 9)3

= 24 cm²

Area of Δ IJN  = (1/2)* IJ * JN  = (1/2) * 9 * (CN  - CJ)

= (1/2) * 9 * (12 - 10)

= 9 cm²

Area of ΔCAN = (1/2) CN * AB

= (1/2) * 12 * 5

= 30 cm²

Area of Pentagon CHINA = 24.5 +  24 + 9 + 30  = 87.5 cm²

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