Chapter 11 Area Of Polygons And Circles

Irregular Figure

A figure which cannot be classified into a specific shape

Irregular Polygon

A polygon that is not regular

Auxiliary line

A segment or line drawn in a figure to aid with analyzing it

Sector

Area in a circle bounded by a central angle and intercepted arc of 2 radii and an intercepted arc

Segment [Circle]

Area in a circle bounded by a chord and arc

Radius^2[π]

Area of a circle

[a^2]2√3

Area of a regular hexagon with given apothem a = apothem

1.5[r^2]√3

Area of a regular hexagon with given radius r = radius

0.5ApothemPerimeter

Area of a regular polygon

360x/r^2[π]

Area of a sector of a circle

s - t

Area of a segment

0.5Height[Base1+Base2]

Area of a trapezoid

0.5BaseHeight

Area of a triangle

0.25[Side^2]√3

Area of an equilateral triangle

0.5Diagonal1Diagonal2

Area of figures with perpendicular diagonals

BaseHeight

Area of parallelogram

#[a^2]Tan[360/2#]

Area of regular polygon with given apothem and number of sides # = number of sides a = apothem

#[r^2]Cos[360/2#]Sin[360/2#]

Area of regular polygon with given radius and number of sides # = number of sides r = radius

Y/X

Geometric probability is probability that involves geometric measure. Formula for the geometric probability of something when X = possible events Y = desired outcome

The Surveyor's Method

Method used to find the area of any polygon using the coordinates of its vertices

Non-Overlapping Parts

Postulate: The area of a region is the sum of its ________

Equal

Postulate: if 2 figures are congruent, then their areas are _____

Apothem

Segment from the center of a circle to a chord