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1

Find the area of the pentagon shown in fig. 20.48, if *AD* = 10 cm, *AG* = 8 cm, *AH* = 6 cm, *AF* = 5 cm, *BF* = 5 cm, *CG* = 7 cm and *EH* = 3 cm.

GH = AG – AH = 8 – 6 = 2 cm

HF = AH – AF = 6 – 5 = 1 cm

GD = AD – AG = 10 – 8 = 2 cm

Area of given figure = area of triangle AFB + area of trapezium BCGF + area of triangle CGD + area of triangle AHE + area of triangle EGD

Area of right angled triangle =

Area of trapezium =

Area of given pentagon =

Area of given pentagon =

Area of given pentagon = = 52.5 cm^{2}

Therefore area of given pentagon is 70 cm^{2}