Polygons and Area

Section 10-1

 A polygon that is both equilateral and equiangular

 If all of the diagonals lie in the interior of the figure, then the polygon is convex.

 If any point of a diagonal lies outside of the figure, then the polygon is concave.

Section 10-2

 If a convex polygon has n sides, then the sum of the measures of its interior angles is (n-2)180

 In any convex polygon, the sum of the measures of the exterior angles, one at each vertex, is 360.

Section 10-3

 For any polygon and a given unit of measure, there is a unique number A called the measure of the area of the polygon

 Congruent polygons have equal areas

 The area of a given polygon equals the sum of the areas of the nonoverlapping polygons that form the given polygon.

Section 10-4

 If a triangle has an area of A square units, a base of b units, and a corresponding altitude of h units, then A = ½ bh

 If a trapezoid has an area of A square units, bases of b 1 and b 2 units, and an altitude of h units, then A = ½ h(b 1 +b 2 )

Section 10-5

 A point in the interior of a regular polygon that is equidistant from all vertices

 A segment that is drawn from the center that is perpendicular to a side of the regular polygon

 If a regular polygon has an area of A square units, and apothem of a units, and a perimeter of P units, then A = ½ aP

 All digits that are not zeros and any zero that is between two significant digits  Significant digits represent the precision of a measurement

Section 10-6

 If you can draw a line down the middle of a figure and each half is a mirror image of the other, it has symmetry

 If you can draw this line, the figure is said to have line symmetry  The line itself is called the line of symmetry

 If a figure can be turned or rotated less than 360° about a fixed point so that the figure looks exactly as it does in its original position, it has rotational or turn symmetry

Section 10-7

 A tiled pattern formed by repeating figures to fill a plane without gaps or overlaps

 When one type of regular polygon is used to form a pattern

 If two or more regular polygons are used in the same order at every vertex