Answer:
The area of the shaded region is 6.88 cm ² (3.44+3.44)
Explanation:
Area of the shaded part = Area of the square - Area of the two semi circles + overlapped yellow area
Area of the square = 4² = 16
r = 4/2 = r=2cm
Area of semicircle = πr²/2
Area of the semicircle = π(2) ²/2
Area of one semicircle = 6.28 cm²
Area of two semi-circles = 2 * 6.28 cm²
Area of two semi-circles = 12.56 cm²
Area of the shaded region = Area of a square - Area of two semicircles (plus overlapped area)
Area of the shaded region (minus overlapped area) = 16 cm² - 12.56 cm²
Area of the shaded region (minus overlapped area) = 3.44
Now we need to add the overlapping area of the 2 semicircles
Area overlapped yellow = 1
The other yellow area =2
White parts= S
The area of 2 semicircles with side length 2 (half of 4) is the same.
The area of the big quarter circle is π*2r*2r/4 = π*r², because its radius is twice as big as the small circles.
S = area of each white as the area of the semicircles is:
π*r²/2 = I + S
So, the area of 1 = π*r²/2 - S. The area of the big quarter circle is:
π*r² = 1 + 2+ S + S
Subtract the area of a semicircle circle, and we have
π*r² - π*r²/2 = 1 + 2 + S + S - 1 - S
π*r²/2 = 2 + S
so 2 = π*r²/2 - S.
That means that the area of 1 and 2 are the same