Lesson 8 4 Areas of Regular Polygons Definition

Lesson 8. 4 Areas of Regular Polygons Definition: An apothem of a regular polygon is a perpendicular segment from the center of the polygon’s circumscribed circle to a side of the polygon. You may also refer to the length of the segment as the apothem. JRLeon Geometry Chapter 8. 4 HGSH

Lesson 8. 4 Areas of Regular Polygons You can divide a regular polygon into congruent isosceles triangles by drawing segments from the center of the polygon to each vertex. The center of the polygon is actually the center of a circumscribed circle, so these congruent segments are sometimes called the radii of a regular polygon. JRLeon Geometry Chapter 8. 4 HGSH

Lesson 8. 4 Areas of Regular Polygons What is the perimeter of a regular polygon in terms of n and s? sn = Perimeter, where s is the side and n is the number of sides. JRLeon Geometry Chapter 8. . 4 HGSH

Lesson 8. 5 Areas of Circles The polygon can be broken down into n isosceles triangles such as the one shown(where n is the number of sides). In this triangle s is the side length of the polygon r is the radius of the polygon and the circle h is the height of the triangle. The area of the triangle is half the base times height: There are n triangles in the polygon. So: The term ns is the perimeter of the polygon (length of a side, times the number of sides). As the number of sides increase, the triangles get smaller and the polygon approaches a circle, where the value of the perimeter approaches the circle circumference, which is 2 r. Also, as the number of sides increases, the triangle gets narrower and narrower, and so when s approaches zero, h and r become the same length. So substituting r for h: = r 2 JRLeon Geometry Chapter 8. . 5 HGSH

Lesson 8. 5 Areas of Circles EXAMPLE A JRLeon Geometry Chapter 8. . 5 HGSH

Lesson 8. 5 Areas of Regular Polygons Areas of Circles Class Work / Home Work: 8. 3 Pages 435 – 436 : problems 1 thru 4, 8 8. 4 Pages 443 – 444 : problems 1 thru 8, 13, 14 8. 5 Pages 451 - 452 : problems 1 thru 10 JRLeon Geometry Chapter 8. 4 -8. 5 HGSH