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Question

Find the area of the region ABCDEFA shown in the given figure, given that ABDE is a square of side 10 cm, BCD is a semicircle with BD as diameter, EF = 8 cm, AF = 6 cm and ∠AFE = 90°.


Solution


Join AE.
Now, AEDB is a square.
Area of the square = Side2 = 102=100 sq. cm

Area of semi-circle = 12πr2=12×3.14×5×5=39.25 cm2

Area of EFA = 12×B×H=12×8×6=24 cm2

Area of the region ABCDEFA = Area of the square + Area of the semicircle - Area of EFA
                                                = 100 + 39.25 - 24                                      
                                                = 115.25 sq. cm

Mathematics
RS Aggarwal (2015)
Standard X

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