Find the coloured area

The area of the shaded region is equal to the area of a semicircle plus the area of a circular segment. The area of the semicircle is $\dfrac{1}{2}\pi (10^2) \approx 157.08$ . The area of the circular segment is equal to the area of the circular sector minus the area of the triangle, we have $\dfrac{135}{360}(\pi)(10^2)-\dfrac{1}{2}(10^2)(\sin 135) \approx 82.45$ . So the desired area is $157.08+82.45=\boxed{239.53}$

Area $=$ Area of circle $-$ area of pie slice $DCF-$ area of triangle $DEC$ .

Area $=100\pi-\frac{45}{360}\cdot100\pi-2\cdot\frac12\cdot10sin(22.5)\cdot 10cos(22.5)=\boxed{239.53}$