Plane Geometric Figures

PLANE GEOMETRIC FIGURES WITH CURVED BOUNDARIES

Circle

Count Circle Formula
Circle

Let
C = circumference
r = radius
D = diameter
A = area
S = arc length subtended by ө
l = chord length subtended by ө
H = maximum rise of arc above chord, r -H = d
ө = central angle (rad) subtended by arc S
C = 2pr = pD (p = 3.14159 . . .)
S = rq = aDq

Formula

Ring (area between two circles of radii r1 and r2 ) The circles need not be concentric, but one of the circles must enclose the other.

A = Π(r1 + r2)(r1 - r2), r1 > r2

Ellipse

Count Ellipse Formula
Ellipse

Let the semiaxes of the ellipse be a and b

A = Πab
C = 4aE(k)

where e2 = 1 - b2/a2 and E(e) is the complete elliptic integral of the second kind,

E(e) = Π/2 {1 – (1/2)2 . e2 + …}

[an approximation for the circumference
Formula-2
Catenary
(the curve formed by a cord of uniform weight suspended freely between two points A, B)

y = a cosh (x/a)

Length of arc between points A and B is equal to 2a sinh (L/a). Sag of the cord is D = a cosh (L/a) - 1.

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