Polygons and Area (Chapter 10)

Polygons (10.1) polygon = a closed figure convex 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 360 o.

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 d 1 d 2 Area of a square = bh or ½ d 1 d 2 Area of a trapezoid = ½ (b 1 +b 2 )h Area of a kite = ½ d 1 d 2 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 = 60 o Angles of squares = 90 o Angles of regular hexagons = 120 o Sides of triangles = x, x  3, 2x Sides of triangles = x, x, x  2

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