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Assignment Assignment P. 740-743: 3- 10, 12, 14, 15, 28, 31, 32, 35 P. 765-768: 1-7, 10-18 even, 17, 19, 23-25, 28, 35, 43, 47, 48 Challenge Problems

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Assignment. P. 740-743: 3-10, 12, 14, 15, 28, 31, 32, 35 P. 765-768: 1-7, 10-18 even, 17, 19, 23-25, 28, 35, 43, 47, 48 Challenge Problems. Example 1. Explain how you could find the area of the regular hexagon shown. Regular Inscribed Polygon. - PowerPoint PPT Presentation

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Page 1: Assignment

AssignmentAssignment

• P. 740-743: 3-10, 12, 14, 15, 28, 31, 32, 35

• P. 765-768: 1-7, 10-18 even, 17, 19, 23-25, 28, 35, 43, 47, 48

• Challenge Problems

Page 2: Assignment

Example 1Example 1

Explain how you could find the area of the regular hexagon shown.

Page 3: Assignment

Regular Inscribed PolygonRegular Inscribed Polygon

The diagram shows a regular polygon inscribed in a circle.– Center of circle =

center of the center of the polygonpolygon

– Radius of circle = radius of the radius of the polygonpolygon

Page 4: Assignment

Regular Inscribed PolygonRegular Inscribed Polygon

The apothemapothem of the polygon is the distance from the center to any side of the polygon.– Apothem = height

of isosceles triangle with 2 radii as legs

Page 5: Assignment

Regular Inscribed PolygonRegular Inscribed Polygon

A central angle central angle of a polygon is an angle formed by two consecutive radii.– Measure of central

angle = 360

n

Page 6: Assignment

11.6: Areas of Regular Polygons11.6: Areas of Regular Polygons11.3: Perimeter and Area of Similar Figures11.3: Perimeter and Area of Similar Figures

Objective:

1. To find the area of a regular n-gon

2. To describe the effects on perimeter and area when dimensions are changed proportionally

Page 7: Assignment

Example 2Example 2

1. Identify the center, a radius, an apothem, and a central angle of the polygon.

2. Find m<XPY, m<XPQ, m<PXQ.

Page 8: Assignment

Example 3Example 3

Assume a regular n-gon has a side length of s and an apothem of a. Find a formula for the area of the regular n-gon.

Page 9: Assignment

Area of a Regular PolygonArea of a Regular Polygon

The area of a regular n-gon with side length s is half the product of the apothem a and the perimeter P.

Page 10: Assignment

Regular 3-gonRegular 3-gon

What is the measure of each central angle in an equilateral triangle? What is the measure of the angle formed by the apothem and the radius of the triangle?

Page 11: Assignment

Regular 4-gonRegular 4-gon

What is the measure of each central angle in a square? What is the measure of the angle formed by the apothem and the radius of a square?

Page 12: Assignment

Regular 5-gonRegular 5-gon

What is the measure of each central angle in a regular pentagon? What is the measure of the angle formed by the apothem and the radius of the pentagon?

Page 13: Assignment

Regular 6-gonRegular 6-gon

What is the measure of each central angle in a regular hexagon? What is the measure of the angle formed by the apothem and the radius of the hexagon?

Page 14: Assignment

Example 4Example 4

Find the area of each regular polygon.

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SummarySummary

Page 16: Assignment

Example 5Example 5

Find the area of each regular polygon.

1. A = 2. A = 3. A =

Page 17: Assignment

Example 6Example 6

Find the area of each regular polygon.

1. A = 2. A =

Page 18: Assignment

Example 7Example 7

Find a formula for the area of a regular hexagon in terms of s, the side length.

Page 19: Assignment

Example 8Example 8

The perimeter of a regular hexagon is 48 cm. What is the area of the hexagon?

Page 20: Assignment

Example 9Example 9

Find the area of the shaded region.

Page 21: Assignment

Example 10Example 10

Rectangle ABCD ~ PQRS with a scale factor of 3:4. Find the perimeter and area of rectangle PQRS.

9

6

R

Q P

S

D

B C

A

Page 22: Assignment

Perimeter of Similar Perimeter of Similar PolygonsPolygonsIf two polygons are similar with the lengths of

corresponding sides in the ratio of a:b, then the ratio of their perimeters is a:b.

b

a

IIPolygon ofPerimeter

IPolygon ofPerimeter

Page 23: Assignment

Area of Similar PolygonsArea of Similar Polygons

If two polygons are similar with the lengths of corresponding sides in the ratio of a:b, then the ratio of their areas is a2:b2.

Page 24: Assignment

Example 11 Example 11

In the diagram ΔABC ~ ΔDEF. Find the indicated ratio.

1.Ratio (red to blue) of the perimeters

2.Ratio (red to blue) of the areas

Page 25: Assignment

Example 12Example 12

Stuart is installing the same carpet in a bedroom and den. The floors of the rooms are similar. The carpet for the bedroom costs $117. Carpet is sold by the square foot. How much does it cost to carpet the den?

Page 26: Assignment

Example 13Example 13

The polygons below are similar. Find the values of x and y.

Page 27: Assignment

AssignmentAssignment

• P. 740-743: 3-10, 12, 14, 15, 28, 31, 32, 35

• P. 765-768: 1-7, 10-18 even, 17, 19, 23-25, 28, 35, 43, 47, 48

• Challenge Problems