Area of the red part?

A hard-level "Area" problem.This shape is called the "shoemaker's knife". Wherever you slide C, the red area comes to AC × CB × π ÷ 4.

GivenAB = 12 cm, AC = 8 cm. A semicircle is drawn on each of AB, AC and CB / π = 3.14

Hints

1. Start with the largest semicircle. Its diameter AB is 12 cm, so the radius is 6 cm and the area is 6 × 6 × 3.14 ÷ 2 = 56.52 cm².
2. Next, the larger of the two cut-out semicircles. Its diameter AC is 8 cm, so the radius is 4 cm and the area is 25.12 cm².
3. The other one has diameter CB = 12 − 8 = 4 cm, radius 2 cm, area 6.28 cm². The point is that AC and CB add up to AB.
4. The red part is the big semicircle minus the two small ones: 56.52 − 25.12 − 6.28

Answer 25.12cm²

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