Post on 04-Jan-2016
Polygons
OBJECTIVES
• Exterior and interior angles• Area of polygons & circles• Geometric probability
PolygonsDefinition: closed figure/ coplanar segments/ sides
have common, non-collinear endpoints/ each segment intersects only at the endpoints
- most polygons will be convex: sides are ‘pushed out’— concave polygons have one vertex ‘pushed in’ the figure
- A ‘regular polygon’ has all sides & all 's
Interior & Exterior AnglesInterior (vertices) with n sides S = sum of
S = 180 (n –2)
Exterior of polygon with n sides
's 's
's Exterior angle Θ360
θ = n
n regular each interior exterior S = Sum of polygon angle angle θ interior angles3 Triangle 60° 120° 180°4 Quadrilateral 90° 90° 360°5 Pentagon 108° 72° 540°6 Hexagon 120° 80° 720°8 Octagon 135° 45° 1080°10 Decagon 144° 36° 1440°n n-gon 180(n-2)/ n 180-interior 180(n-2)
ParallelogramsDefinition: 2 pairs of parallel sidesany side can be a base for each base there is an altitude (or height)
AREA A = base • height = b h
Area of a complex region is the sum of its non-overlapping parts
h
Area of rhombi, triangles, & trapezoids • Congruent figures have equal areas
• Area of a triangleA = ½ b h
• Area of a trapezoid
A = ½ h (b1 + b2)
• Area of a rhombus
A = d1d2
h
base
h
b1
b2
d1 d2
Regular polygons and circlesAn apothem --center to side( | bisector)A radius of a polygon--center to vertexPerimeter of a polygon—sum of sides
Area regular polygon
A = ½ Perimeter • apothem = ½ Pacircles
A = π r2 radius
ra
Geometric probability =
Segment:: If C is between A & B, the probability of being on AC :
Polygon: Given random point C and rectangle A, the probability that C is in triangle B:
Circle: area of a sector = (N = central angle, r = radius) Probability of being in certain sector(s) =
successful area
total area
•A
•B
•Clength of AC
P = length of AB
area of BP =
area of A ABB
2N
360r
area of sector(s)P =
area of circle