Answer:
This shaded region is consisted of 2 shapes: a right triangle and a semi-circle. To find the overall area, we must first find the are of the 2 shapes and add them together.
Explanation:
1. Find the area of the right triangle:
a = 14, b = 2r = 8cm
A1 = ab/2 = 112/2 = 56cm²
2. Find the area of the circle:
r = 4 cm
A2 = πr² = 3.14 × 4² = 50.24cm²
3. Divide the area of the circle to get the area of the semi-circle:
A3 = A2/2 = 50.24/2 = 25.12cm²
4. Add the areas of the right triangle and the semi-circle together:
A1 + A3 = 56 + 25.12 = 81.12cm²