Assignment
description
Transcript of Assignment
![Page 1: Assignment](https://reader035.fdocuments.us/reader035/viewer/2022062314/56813d5f550346895da72d67/html5/thumbnails/1.jpg)
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](https://reader035.fdocuments.us/reader035/viewer/2022062314/56813d5f550346895da72d67/html5/thumbnails/2.jpg)
Example 1Example 1
Explain how you could find the area of the regular hexagon shown.
![Page 3: Assignment](https://reader035.fdocuments.us/reader035/viewer/2022062314/56813d5f550346895da72d67/html5/thumbnails/3.jpg)
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](https://reader035.fdocuments.us/reader035/viewer/2022062314/56813d5f550346895da72d67/html5/thumbnails/4.jpg)
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](https://reader035.fdocuments.us/reader035/viewer/2022062314/56813d5f550346895da72d67/html5/thumbnails/5.jpg)
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](https://reader035.fdocuments.us/reader035/viewer/2022062314/56813d5f550346895da72d67/html5/thumbnails/6.jpg)
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](https://reader035.fdocuments.us/reader035/viewer/2022062314/56813d5f550346895da72d67/html5/thumbnails/7.jpg)
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](https://reader035.fdocuments.us/reader035/viewer/2022062314/56813d5f550346895da72d67/html5/thumbnails/8.jpg)
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](https://reader035.fdocuments.us/reader035/viewer/2022062314/56813d5f550346895da72d67/html5/thumbnails/9.jpg)
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](https://reader035.fdocuments.us/reader035/viewer/2022062314/56813d5f550346895da72d67/html5/thumbnails/10.jpg)
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](https://reader035.fdocuments.us/reader035/viewer/2022062314/56813d5f550346895da72d67/html5/thumbnails/11.jpg)
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](https://reader035.fdocuments.us/reader035/viewer/2022062314/56813d5f550346895da72d67/html5/thumbnails/12.jpg)
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](https://reader035.fdocuments.us/reader035/viewer/2022062314/56813d5f550346895da72d67/html5/thumbnails/13.jpg)
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](https://reader035.fdocuments.us/reader035/viewer/2022062314/56813d5f550346895da72d67/html5/thumbnails/14.jpg)
Example 4Example 4
Find the area of each regular polygon.
![Page 15: Assignment](https://reader035.fdocuments.us/reader035/viewer/2022062314/56813d5f550346895da72d67/html5/thumbnails/15.jpg)
SummarySummary
![Page 16: Assignment](https://reader035.fdocuments.us/reader035/viewer/2022062314/56813d5f550346895da72d67/html5/thumbnails/16.jpg)
Example 5Example 5
Find the area of each regular polygon.
1. A = 2. A = 3. A =
![Page 17: Assignment](https://reader035.fdocuments.us/reader035/viewer/2022062314/56813d5f550346895da72d67/html5/thumbnails/17.jpg)
Example 6Example 6
Find the area of each regular polygon.
1. A = 2. A =
![Page 18: Assignment](https://reader035.fdocuments.us/reader035/viewer/2022062314/56813d5f550346895da72d67/html5/thumbnails/18.jpg)
Example 7Example 7
Find a formula for the area of a regular hexagon in terms of s, the side length.
![Page 19: Assignment](https://reader035.fdocuments.us/reader035/viewer/2022062314/56813d5f550346895da72d67/html5/thumbnails/19.jpg)
Example 8Example 8
The perimeter of a regular hexagon is 48 cm. What is the area of the hexagon?
![Page 20: Assignment](https://reader035.fdocuments.us/reader035/viewer/2022062314/56813d5f550346895da72d67/html5/thumbnails/20.jpg)
Example 9Example 9
Find the area of the shaded region.
![Page 21: Assignment](https://reader035.fdocuments.us/reader035/viewer/2022062314/56813d5f550346895da72d67/html5/thumbnails/21.jpg)
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](https://reader035.fdocuments.us/reader035/viewer/2022062314/56813d5f550346895da72d67/html5/thumbnails/22.jpg)
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](https://reader035.fdocuments.us/reader035/viewer/2022062314/56813d5f550346895da72d67/html5/thumbnails/23.jpg)
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](https://reader035.fdocuments.us/reader035/viewer/2022062314/56813d5f550346895da72d67/html5/thumbnails/24.jpg)
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](https://reader035.fdocuments.us/reader035/viewer/2022062314/56813d5f550346895da72d67/html5/thumbnails/25.jpg)
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](https://reader035.fdocuments.us/reader035/viewer/2022062314/56813d5f550346895da72d67/html5/thumbnails/26.jpg)
Example 13Example 13
The polygons below are similar. Find the values of x and y.
![Page 27: Assignment](https://reader035.fdocuments.us/reader035/viewer/2022062314/56813d5f550346895da72d67/html5/thumbnails/27.jpg)
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