Areas of Polygons and Circles

geometric probability

A probability that involves a geometric measure such as length or area.

segment

a measurement part of a line that consists of two points, called endpoints, and all of the points between them

apothem

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

Postulate 11.1

congruent figures have equal areas

irregular figure

figure that cannot be classified into the specific shapes that we have studied

Area of a Circle

if a circle has an area of A square units and a radius of r units, then A=pie r2

Area of a Parallelogram (key concept)

if a parallelogram has an area of A square units, a base of b units, and a height of h units, then A=bh

Probability and Area (key concept)

if a point in region A is chosen at random, then the probability P(B) that the point is in region B, which is in the interior of region A, is P(B)= area of region B/ area of region A

Area of a Regular Polygon (key concept)

if a regular polygon has an area of A square units, a perimeter of P units, and an apothem of a units, then A=1/2Pa

Area of a Rhombus (key concept)

if a rhombus has an area of A square units and diagonals of d1 and d2 units, then A=1/2d1d2

Area of a Sector (key concept)

if a sector of a circle has an area of A square units, a central angle measuring N degrees, and a radius of r units, then A= N/360 pie r2

Area of a Trapezoid (key concept)

if a trapezoid has an area of A square units, bases of b1 units and b2 units, and a height of h units, then A=1/2h(b1+b2)

Area of a Triangle (key concept)

if a triangle has an area of A square units, a base of b units, and a corresponding height of h units, then A=1/2bh

irregular polygon

polygon without all congruent sides

Postulate 11.2

the area of a region is the sum of the areas of all its nonoverlapping parts

sector of a circle

the region bounded by two radii of the circle and their intercepted arc