Download 11 - Wsfcs

11.1 Angle Measures in Polygons
Polygon Interior Angles Theorem: the sum of the measures of the interior angles
of a convex n-gon is (n – 2)180˚.
The measure of each interior angle of a regular n-gon is (n – 2)180˚ / n.
Polygon Exterior Angles Theorem: the sum of the measures of the exterior angles
of a convex polygon, one at each vertex, is 360˚.
The measure of each exterior angle of a regular n-gon is 360˚ / n.
Find the value of x in each polygon.
Find the sum of the measures of the interior angles of the convex polygon.
10-gon
102-gon
15-gon
50-gon
Given the measure of each interior angle, determine the type of polygon.
150˚
160˚
157.5˚
175˚
Given the number of sides of regular polygon, find the exterior angle measure.
Use exterior angle = 360˚ / number of sides
15
36
8
10
Given the measure of the exterior angle of a regular n-gon, find the number of
sides. Use number of sides = 360˚ / exterior angle.
20
40
5
36
Page 665: 1 – 8 in class; 9 – 25, 29 - 41
11.2 Areas of Regular Polygons
Area of an Equilateral Triangle: the area of an equilateral triangle is one forth the
square of the length of the side times the square root of three.
A = s²√3
4
Area of a Regular Polygon: the area of a regular polygon with side length s is one
half the product of the apothem, a, and the perimeter, P.
A=½aP
To find the apothem, you may need to use the tangent ratio.
Find the perimeter and area of each regular polygon.
First Period: Page 672: 1 – 24, 27 - 32
Second, Third, and Fifth Periods: page 672: 1 – 24
11.3 Perimeters and Areas of Similar Figures
Areas of Similar Polygons: if two polygons are similar with the lengths of
corresponding sides in the ration of a:b, then the ratio of their areas is a²:b².
Side
Side
a
b
Area
Area
a²
b²
The given figures are similar. Find the ratio of their perimeters and areas.
First: 679: 1 – 29, omit 22
Second, Third, Fifth: 679: 1 – 18, 23 – 28 all
11.4 Circumference and Arc Length
Circumference of a circle is the distance around the circle. The ratio of the
circumference to the diameter is the same for all circles. This ratio is pi.
Circumference of a Circle: the circumference C of a circle is C = πd or C= 2πr.
Arc length is a portion of the circumference of a circle.
Arc Length Corollary: in a circle, the ratio of the length of a given arc to the
circumference is equal to the ratio of the measure of the arc to 360˚.
Arc Length = mAB • 2πr
360
Find the arc lengths of the following circles.
Use the arc lengths to find the indicated measure.
Circumference =
Circumference =
Length of AB =
Radius =
First and Second Periods: page 686: 1 - 32
Third and Seventh Periods: page 686: 1 – 29
11.5 Areas of Circles and Sectors
Area of a Circle is π times the square of the radius, or A = πr².
Find the area of the circles.
Area of a Sector
The ratio of the area of a sector of a circle to the area of the circle is equal to
the ratio of the measure of the intercepted arc to 360˚.
A = mAB • πr²
360
Find the area of each sector.
695: 1 – 20, 23 – 28, omit 25
11.6 Geometric Probability
A probability is a number from 0 to 1 that represents the chance that an event
will occur.
Assuming all outcomes are equally likely:
an event with a probability of 0 cannot occur,
an event with a probability of 1 is certain to occur,
an event with a probability of 0.5 is just as likely to occur as not.
Probability and Length
Let AB be a segment that contains the segment CD. If a point K on AB is chosen
at random, then the probability that it is on CD is as follows:
P(Point K is on CD) = Length of CD
Length of AB
Probability and Area
Let J be a region that contains region M. IF a point K is chosen at random, then
the probability that it is in region M is as follows:
P(Point K is in region M) = Area of M
Area of J
Open your books to page 699 for further examples.
Chapter 11 Test on Thursday
Class work: page 701: 1 – 20 all
Homework: page 702: 21 – 42 all
Chapter 11 Test on Thursday !!!