Length of BC = BF = 2

Area of square BCFE = 4

Area of Circle (unshaded part which overlaps Square) = 2 * 1/2 * pie * r^2 = pie

Shaded region area = 4- pie = ~1

E
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The area of the shaded region equals
(Rectangle area) - (circles' area)/2

Rectangle area: L * W
The circles' radii completely span the length and width of the rectangle
Radius of one circle = 1

LENGTH = 4 radii = 4
WIDTH = 2 radii = 2
Rectangle's area = 4 * 2 = 8

Area of both circles, where r = 1: \(2(πr^2) = 2π\)

Area of shaded region
The "extra" area between the rectangle's edges and the circles' edges consists of 8 equal regions. See diagram.
Four of 8 are shaded = 1/2 of extra is shaded.

To get total extra area, subtract circles' area from rectangle's area.
To get half the total extra area (shaded region), subtract circles' area from rectangle's area and divide by 2.

Half of extra area = area of shaded region:

(rectangle area, R) - (circles' area, C) divided by 2:

\(\frac{(R - C)}{2}\)

\(\frac{(8 - 2π)}{2}\)

\(π\approx{3.14}\)

\(\frac{(8 - 6.28)}{2}= \frac{1.72}{2} = .86\)

\(0.86\approx{1}\)

Answer E
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Inside square has a an area of 4.
Subtract 2 half pokeballs from 4, so subtract one full pokeball.
Square Area 4 - Pokeball area of 3.1 = .9 shaded or E.

We can see that the area of the shaded region is half the area of the region inside of the rectangle but outside of the two circles. Thus, the area of the shaded region is half the difference between the area of the rectangle and the total area of the two circles.

Area of the rectangle = 2 x 4 = 8

Area of a circle = π x 1^2 = π

Area of shaded region = ½ x (8 - 2π) = 4 - π

Since π is approximately 3.14, the area of the shaded region ≈ 4 - 3.14 = 0.86 ≈ 1.

Answer: E
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Area of rectangle 2x4=8
Are of each circle is π
Area of the segments inside the rectangle that are outside the circles is 8-2π ≈ 2, hence the shaded region has to be less than 2. Only answer E is left.