1 / 12

Agenda

Agenda. 1 st block 45-45-90 and 30-60-90 triangle worksheet Notes 11-4 Classwork due by end of class. 3 rd block Pop quiz Go over homework from Wednesday night Notes 11-4 Classwork due by end of class. Areas of Regular Polygons. 11-4. Goals/Purpose.

alima
Télécharger la présentation

Agenda

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Agenda • 1st block • 45-45-90 and 30-60-90 triangle worksheet • Notes 11-4 • Classwork due by end of class • 3rd block • Pop quiz • Go over homework from Wednesday night • Notes 11-4 • Classwork due by end of class

  2. Areas of Regular Polygons 11-4

  3. Goals/Purpose • At the completion of the lesson, you will be able to… • identify and calculate the center, radius, apothem, and central angle of a regular polygon • Calculate the area of a regular polygon • We are studying this material because regular polygons are common in structures and buildings

  4. Definitions • Center – the center of the circle circumscribed about the polygon • radius – a segment drawn from the center of a polygon to a vertex • apothem – a segment drawn from the center of a polygon that is perpendicular to a side • central angle – an angle formed by two radii drawn to consecutive vertices

  5. Theorem 11.6 Area of a Regular Polygon • The area of a regular n-gon with side lengths (s) is half the product of the apothem (a) and the perimeter (P), so A = ½ aP, or A = ½ a • ns. NOTE: In a regular polygon, the length of each side is the same. If this length is (s), and there are (n) sides, then the perimeter P of the polygon is n • s, or P = ns The number of congruent triangles formed will be the same as the number of sides of the polygon.

  6. More . . . • A central angle of a regular polygon is an angle whose vertex is the center and whose sides contain two consecutive vertices of the polygon. You can divide 360° by the number of sides to find the measure of each central angle of the polygon. • 360/n = central angle

  7. A regular pentagon with radius 1 unit. Find the area of the pentagon. Ex: Finding the area of a regular polygon C 1 B D 1 A

  8. Solution: • you must find the apothem (or if the apothem was given, you must find the radius, etc) • You need to find measure of central angle. ABC is 360°/5, or 72°.

  9. Solution: • Draw the apothem. It is an isosceles triangle so it bisects the angle. • You now have a right triangle and can use trig ratios to find the missing sides 36°

  10. Solution

  11. You try….. • Find the area of a regular polygon with 9 sides and a radius of 10

  12. Homework • Page 442 1-8

More Related