Excuse me: how to find out the area of a semicircle with a diameter of 8 cm

Excuse me: how to find out the area of a semicircle with a diameter of 8 cm

Connect CD, BD, OD
The area of the whole figure
=Area of isosceles right triangle ABC + area of semicircle
=(10*10/2)+3.14*(10/2)*(10/2)/2
=50+39.25
=89.25 square centimeter
The area of the shaded area
=Area of the whole figure - area of triangle ACD - area of arch CD
=Area of the whole figure - area of ACD of triangle - half area of semicircle + area of COD of triangle
Isosceles right triangle ABC, angle ACB = 45 degrees, AC = 10 times root 2
D is the midpoint of the circle, BC is the diameter of the semicircle,
So triangle BCD is also isosceles right triangle, CD = 5 times root 2, angle BCD = 45 degrees
So angle ACD = angle ACB + angle DCB = 45 + 45 = 90 degrees
So ACD is a right triangle, its area = (5 times root 2) * (10 times root 2) / 2 = 50 square centimeter
Area of half circle = 3.14 * (10 / 2) * (10 / 2) / 4 = 19.625
Triangle cod is also isosceles right triangle, CO = od = = 5, its area = 5 * 5 / 2 = 12.5, so
The area of the shaded area
=Area of the whole figure - area of ACD of triangle - half area of semicircle + area of COD of triangle
=89.25-50-19.625+12.5
=32.125 square centimeter