CHAPTER 10

Polygons and Area

NAMING POLYGONS

Section 10-1

REGULAR POLYGONA polygon that is both equilateral and equiangular

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

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

DIAGONALS AND ANGLE

MEASURE

Section 10-2

THEOREM 10-1 If a convex polygon has n sides, then the sum of the measures of its interior angles is

(n-2)180

THEOREM 10-2 In any convex polygon, the sum of the measures of the exterior angles, one at each vertex, is 360.

AREAS OF POLYGONS

Section 10-3

POSTULATE 10-1For any polygon and a given unit of measure, there is a unique number A called the measure of the area of the polygon

POSTULATE 10-2Congruent polygons have equal areas

POSTULATE 10-3The area of a given polygon equals the sum of the areas of the nonoverlapping polygons that form the given polygon.

AREAS OF TRIANGLES

AND TRAPEZOIDS

Section 10-4

THEOREM 10-3 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

THEOREM 10-4 If a trapezoid has an area of A square units, bases of b1 and b2 units, and an altitude of h units, then

A = ½ h(b1 +b2)

AREAS OF REGULAR

POLYGONS

Section 10-5

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

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

THEOREM 10-5 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

SIGNIFICANT DIGITS All digits that are not zeros and any zero that is between two significant digits

Significant digits represent the precision of a measurement

SYMMETRYSection 10-6

SYMMETRY 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

LINE SYMMETRY If you can draw this line, the figure is said to have line symmetry

The line itself is called the line of symmetry

ROTATIONAL 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

TESSELLATIONS

Section 10-7

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

REGULAR TESSELLATION

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

SEMI-REGULAR TESSELLATION

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