Yellow area minus blue area

Geometry Level pending

Four identical circles, each of radius $1$ , are drawn at the vertices of a square of side length $4$ . If $y$ represents the area of the yellow region and $b$ represents the area of the blue region, find $y-b$ .

-3\pi+16

16+2\pi

8-\pi

4(4-\pi)

1 solution

Wind Quotidian
Nov 16, 2017

The four quarter circles in the square area can be considered as a whole circle in the square. The area of one complete circle would be pi X (1^2) . Given that the side length of the square is 4, the area of the square is 4 X 4 and the area of the yellow region can be described as 4 X 4 - pi . The blue region are made up of four $\frac{3}{4}$ circles, which, also, can be considered as three whole circles. Therefore, the area of the blue region is 3 X pi .

Thus, the area of y - b is 4 X 4 - pi - 3 X pi , which we can simplify and factorize into 4(4 - pi) .

Yellow area minus blue area

1 solution

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