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 = ${\mathrm{Side}}^{2}$ =  Area of semi-circle = $\frac{1}{2}{\mathrm{\pi r}}^{2}$= Area of $∆$EFA =  Area of the region ABCDEFA = Area of the square + Area of the semicircle $-$ Area of $∆$EFA                                                 = 100 + 39.25 $-$ 24                                                                                       = 115.25 sq. cmMathematicsRS Aggarwal (2015)Standard X

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