Polygons OBJECTIVES Exterior and interior angles Area of polygons & circles Geometric probability

Polygons Definition: 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

Interior & Exterior Angles Interior (vertices) with n sides S = sum of S = 180 (n –2) Exterior of polygon with n sides  Exterior angle Θ n regular each interior exterior S = Sum of polygon angle angle θ interior angles 3 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-interior180(n-2)

Parallelograms Definition: 2 pairs of parallel sides any 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 triangle A = ½ b h Area of a trapezoid A = ½ h (b 1 + b 2 ) Area of a rhombus A = d 1 d 2 h base h b1b1 b2b2 d 1   d2 d2

Regular polygons and circles An apothem --center to side( | bisector) A radius of a polygon--center to vertex Perimeter of a polygon—sum of sides Area regular polygon A = ½ Perimeter apothem = ½ Pa circles A = π r 2  radius r a

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) = A B C A BB