Arc area formula

Arc area formula

S sector = (LR) / 2 (L is the sector arc length) = (θ ° R ^ 2) / 2 (θ is the center angle in radians)
S sector = (n / 360) π R ^ 2 (n is the degree of the center angle of the circle, R is the radius of the bottom circle)
Note: π is pi

The area formula of semicircle arc

Calculation formula of semicircle arc area = circumference * square of radius * center angle of circle / 360
The "*" sign is the multiplication sign and the "/" sign is the division sign

Calculation formula of circular arc area

You mean bow
When the arc of the bow is inferior:
If the radius is R and the height is h, then the center angle a can be obtained
cos(a/2)=(r-h)/r
The area of the sector is
πr^2*(a/360)
The triangle area is:
(1/2)*(2rsin(a/2))*(r-h)
=(r-h)*r*sin(a/2)
Subtracting the area of the upper triangle from the sector area is the area you want
πr^2*(a/360)-(r-h)*rsin(a/2)
When the arc of bow is superior arc:
Then the area of the other part is calculated first. The method is the same as above, but the height is changed to (2r-h);
Calculate another part of the bow area and subtract it from the circle
If you know the center angle of the circle, it is more convenient to calculate