Question

I just need help with finding the yellow (shaded) region. I also need a good explanation because I am SO LOST!

Answer 1

Answer:

The area of the shaded region is 6.88 cm ² (3.44+3.44)

Step-by-step 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