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9 2 Developing Formulas for Circles and Regular Polygons.notebook
1
February 24, 2012
Apr 53:50 PM
February 24, 2012
9.2 Formulas for Circles and Regular Polygons
Objectives:
1. Find circumference and Area of a circle.2. Find the area of any regular polygon.
Tweedledeedum and Tweedledeedee,Around the circle is pi times d,But if the area is declared,
Think of the formula π "r" squared.
SPI 3108.4.7 Compute the area and/or perimeter of triangles, quadrilaterals and other polygons when one or more additional steps are required (e.g. find missing dimensions given area or perimeter of the figure, using trigonometry).
Checks for Understanding 3108.4.28 Derive and use the formulas for the area and perimeter of a regular polygon.
Responsible Pet Owner Month!
Feb 2311:23 AM
A circle is the locus of points in a plane that are a fixed distance from a point called the center of the circle.
A circle is named by the symbol ¤ and its center.
¤A has radius r = AB and diameter d = CD.
Feb 2311:34 AM
To have an EXACT final answer you will keep the pi symbol.
If the problem asks you to round, use the pi key on your handheld at the very end.
Feb 2311:15 AM
With a neighbor work on the following:
Find the area of ¤K in terms of π. A = 9π in2
Find the radius of ¤J if the circumference is (65x + 14)π m.
Find the circumference of ¤M if the area is 25 x2π ft2
C = 10xπ ft
r = (32.5x + 7) m
Feb 2311:39 AM
The center of a regular polygon is equidistant from the vertices.
A central angle of a regular polygon has its vertex at the center, and its sides pass through consecutive vertices.
What would be measure of each central angle of a regular ngon be?
The apothem is the distance from the center to a side. What will the apothem represent in each of the triangles?
Will all the triangles be congruent to each other always? Explain.
Apr 55:46 PM
We know that the area of the regular polygon will be:
A = area of one triangle number of triangles
We can use this to find the area of any regular ngon by dividing the polygon into congruent triangles.
A = area of one triangle number of triangles
= (½ apothem side length s) number of sides
= ½ apothem side length s number of sides
= ½ apothem perimeter of polygon
Area of a Regular Polygon
The area of a regular ngon with side lengths s is half the product of the apothem a and the perimeter P, so A = ½aP, or A = ½ans
9 2 Developing Formulas for Circles and Regular Polygons.notebook
2
February 24, 2012
Apr 56:35 PM
Example 3: Finding the Area of a Regular Polygon
Find the area of a regular hexagon with side length 10 cm.
10 cm
See Video Example 3
Feb 231:54 PM
Example 4: Finding the Area of a Regular Polygon
Find the area of a regular octagon with side length 3 cm.
3 cm
See Video Example 3
Feb 231:58 PM
In the past two examples we have only been given the side length, what occurs if we are given the apothem length instead?
Find the area of the regular polygon.
Apr 59:09 PM
Assignment:
Page 603
#'s 10 12, 14, 17 19, 22, 24 26, 28 30, 33, 40(16 problems)
Draw all pictures and show work!
Apr 149:32 AM