Polygons and Area

(Chapter 10)

Polygons (10.1)

polygon = a closed figureconvex polygon = a polygon such

that no line containing a side goes through the interior of the polygon

regular polygon = a convex polygon with all sides congruent and all angles congruent

Interior Angle Sum Theorem

If a convex polygon has n sides, then the sum of the measures of the interior

angles is (n 2) · 180 .

Exterior Angle Sum Theorem

In a convex polygon, the sum of the measures of the exterior angles (one at each vertex) is 360o.

Area Formulas (10.1)

Area of a parallelogram = bh

(b = base, h = height)

Base and height must be perpendicular to each other.

Area of a triangle = ½ bh

Area of a rectangle = bh

Area of a rhombus = ½ d1d2

Area of a square = bh or ½ d1d2

Area of a trapezoid = ½ (b1+b2)h

Area of a kite = ½ d1d2

Area Formulas (10.2)

Area Formulas (10.3)

Area of a regular polygon =

½ aP

(a = apothem, P = perimeter)

apothem = a segment from the center of a regular polygon to the midpoint of a side

What you need to recall:

Regular polygons have all sides equal and all angles equal.

Angles of equilateral triangles = 60o

Angles of squares = 90o

Angles of regular hexagons = 120o

Sides of 30-60-90 triangles = x, x3, 2xSides of 45-45-90 triangles = x, x, x2

What is new:

radius = a segment from the center of a regular polygon to a vertex

The angle formed by two consecutive radii = 360 ÷ n.(n = number of sides)

The triangle formed by two consecutive radii is isosceles.

Tessellations (10.2)

tessellation = a pattern that covers a plane with repeating figures so there is no overlapping or empty spaces

regular tessellation = a tessellation that uses only one type of regular polygon

semi-regular tessellation = a tessellation that uses two or more regular polygons

uniform tessellation = a tessellation containing the same combination of shapes at each vertex