a.
To find: The half side x of the
Required value of x is
Given Data:
The hexagon is shown in Fig.1.
Method/Formula Used:
In a right angle triangle
Calculations:
In right angle triangle OAM shown in Fig. 1,
Substitute x for AM, 1 for AM, and
AB is the side of hexagon, also the chord of the circle of radius 1 in which the hexagon is inscribed.
Thus, the side of the hexagon is 1, there are total 6 equal sides in the hexagon. Therefore, the perimeter p of the hexagon is,
The perimeter of the hexagon is 6 units.
b.
To show: A regular n -sided polygon inscribed in a circle of radius 1 has perimeter of
Given data:
The polygon inscribed in a unit circle has n sides.
Method used:
The triangle ABC formed in an n -sided polygon inscribed in unit circle is makes angle
Proof:
Let AB is one side of n-sided polygon. The side makes angle
AB is the side of polygon given by
There are total n equal sides in the hexagon. Therefore, the perimeter p of the polygon is,
Substitute
But
Hence, proved.
c.
To find: The result in part (b) in terms of
Given:
The perimeter of n -sided polygon is
Method used:
The angle made by a circle at its center is
Calculations:
The perimeter p of n -sided polygon is
Since,
Substitute
When n is large, the angle
Substitute
Thus, the perimeter of polygon is equal to the circumference of the unit circle.
The perimeter of the 50 sided polygon is,
Chapter 9 Solutions
Holt Mcdougal Larson Algebra 2: Student Edition 2012
- Algebra and Trigonometry (6th Edition)AlgebraISBN:9780134463216Author:Robert F. BlitzerPublisher:PEARSONContemporary Abstract AlgebraAlgebraISBN:9781305657960Author:Joseph GallianPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
- Algebra And Trigonometry (11th Edition)AlgebraISBN:9780135163078Author:Michael SullivanPublisher:PEARSONIntroduction to Linear Algebra, Fifth EditionAlgebraISBN:9780980232776Author:Gilbert StrangPublisher:Wellesley-Cambridge PressCollege Algebra (Collegiate Math)AlgebraISBN:9780077836344Author:Julie Miller, Donna GerkenPublisher:McGraw-Hill Education