Quadrilaterals, Polygons - Regular Polygons
     
      Cyclic quadrilateral
      Tangential quadrilateral
     Polygons
     Regular polygons
Cyclic quadrilateral
A quadrilateral inscribed in a circle, so that all its vertices lie on the circumference is called a cyclic quadrilateral.
The opposite angles of a cyclic quadrilateral are supplementary.
 
a + g = b + d = 180,
d1  d2  = a    c + b  d
perimeter    P = a + b + c + d,     s = 1/2
area
Tangential quadrilateral
A quadrilateral whose sides all lie tangent to the circle inscribed within the quadrilateral is called a tangential quadrilateral.
 
s = a + c = b + d,
perimeter    P = a + b + c + d,     s = 1/2
area A = r s
Polygons
A polygon is closed plane figure bounded by a number of straight line segments with the same number of vertices.
The sum of interior angles is  (n - 2) 180, where n is the number of sides of a polygon. 
The sum of exterior angles of a polygon is 360.
 
 dn - number of diagonals
b' - the exterior angle
dn = 1/2 n (n - - 3)
Sn= (n - 2) 180 - the sum of interior angles
Regular polygons
In a regular polygon all sides are equal and all its angles are equal.
The exterior angle of a regular polygon is b' = 360/n, where n is the number of sides of a regular polygon. .
 a = b' = 360/n b' - the exterior angle
b = 180 - b' = (n - 2) 180/n,     P = n a
dn = 1/2 n (n - - 3) - number of diagonals
A = 1/2 n a r = 1/2P r - area of a regular polygon
Beginning Algebra Contents D
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