New Problem (Level 1) : Geometry (Plane figure) Problem 3 TOYOEIWA-2008

The figure below is a graphic drawn with semicircles with radii 2 cm and 4 cm. 

Find the area of the portion of the shadow. 

Pi is assumed to be 3.14.






Answer
67.4 cm2

Solution

4 × (2 + 8) - 2 × 2 + 4 × 4 × 3.14 × 1/2 + 4 × 4 × 3.14 × 1/4 - 2 × 2 × 3.14 × 1/2
= 40 - 4 + (8 + 2) × 3.14 = 36 + 31.4 =67.4 cm2