# 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°.

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. cm

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