Answer:
12.53
Step-by-step explanation:
∠BCA = (180°-40°)/2 = 70°
Laws of Sines: CA/sin 40° = AB/sin 70° = 5/sin 70°
CA = 5/sin 70° * sin 40° = 3.40
area of semicircle CA = (3.1416 * 1.70²) / 2 = 4.54
By Heron's Formula, area of triangle ABC:
1/4 √(a+b+c) (a+b-c) (b+c-a) (c+a-b) = 1/4 * √13.4*3.4*3.4*6.6
= 7.99
Entire region area = 4.54 + 7.99 = 12.53
