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9.2 ­ Developing Formulas for Circles and Regular Polygons Day 1.notebook March 03, 2015
9.2 ­ Formulas for Circles and Regular Polygons
March 3/4, 2015
9.2.1 – I can develop and apply the formulas for the area and circumference of a circle.
9.2.2 – I can develop and apply the formula for the area of a regular polygon.
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9.2 ­ Developing Formulas for Circles and Regular Polygons Day 1.notebook March 03, 2015
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.
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9.2 ­ Developing Formulas for Circles and Regular Polygons Day 1.notebook March 03, 2015
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.
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9.2 ­ Developing Formulas for Circles and Regular Polygons Day 1.notebook March 03, 2015
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.
r = (32.5x + 7) m
Find the circumference of ¤M if the area is 25 x2π ft2
C = 10xπ ft
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9.2 ­ Developing Formulas for Circles and Regular Polygons Day 1.notebook March 03, 2015
The center of a regular polygon is equidistant from the vertices. Will all the triangles be congruent to each other always? Explain.
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?
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9.2 ­ Developing Formulas for Circles and Regular Polygons Day 1.notebook March 03, 2015
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
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9.2 ­ Developing Formulas for Circles and Regular Polygons Day 1.notebook March 03, 2015
Example 3: Finding the Area of a Regular Polygon
Find the area of a regular hexagon with side length 10 cm.
See Video Example 3
10 cm
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9.2 ­ Developing Formulas for Circles and Regular Polygons Day 1.notebook March 03, 2015
Example 4: Finding the Area of a Regular Polygon
Find the area of a regular octagon with side length 3 cm.
See Video Example 3
3 cm
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9.2 ­ Developing Formulas for Circles and Regular Polygons Day 1.notebook March 03, 2015
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.
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9.2 ­ Developing Formulas for Circles and Regular Polygons Day 1.notebook March 03, 2015
Assignment:
Page 603
Standard 9.2.1 – #’s 10 – 12, 33, 40
Standard 9.2.2 – #’s 14, 17 – 19, 22, 24 – 26, 28 – 30 (16 problems)
Draw all pictures and show work!
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9.2 ­ Developing Formulas for Circles and Regular Polygons Day 1.notebook March 03, 2015
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