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°.

Answer 1

Join AE.
Now, AEDB is a square.
Area of the square = ${\mathrm{Side}}^2$ = ${10}^2=100\mathrm{sq}.\mathrm{cm}$

Area of semi-circle = $\frac{1}{2}{\mathrm{\pi r}}^2$=$\frac{1}{2}\times 3.14\times 5\times 5=39.25{\mathrm{cm}}^2$

Area of $∆$EFA = $\frac{1}{2}\times B\times H=\frac{1}{2}\times 8\times 6=24{\mathrm{cm}}^2$

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