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현재 위치

The area when drawing a quadrant around each vertex of a square

작성자 Uploader : 사이다 작성일 Upload Date: 2019-02-22변경일 Update Date: 2019-02-27조회수 View : 279

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As shown in the figure, when drawing a quadrant centered on each vertex of a square with a side length r, the area of each part denoted by a, b, c can be obtained as follows.

Both ends of the base line and the point where arcs from the ends of the base line meet make an equilateral triangle of which side length is r.

Area of equilateral triangle: At = (3^(1/2)/4) * r^2

Since an angle of an equilateral triangle is 60 degrees, the angle formed by one side of the equilateral triangle and the vertical side of the square is 30 degrees.

Area of arc between vertical side and triangle: As = (1/12) * πr^2

Area of "a" : a = r^2 - At - 2*As

Area of the square : Ar = r^2 = 4*a + 4*b + c

Area of the quadrant : Ac = (1/4)*π*r^2 = 2*a + 3*b + c

If c is canceled in both equations, the following equation can be obtained.

2*a + b = r^2 - (1/4)*π*r^2

Thus, "c" is as follows.

Area of all "a" parts

Area of all "b" parts

Area of all "b" and "c" parts

Area of all "a", "b" and "c" parts

n/a

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1st Step for All

현재 위치

The area when drawing a quadrant around each vertex of a square

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