1 / 12

Area and Perimeter: Areas of Regular Polygons

Area and Perimeter: Areas of Regular Polygons. inscribed polygon circumscribed circle. Review: Inscribed Polygons & Circumscribed Circles. Inscribed means written inside. Circumscribed means written around (the outside).

mallory-daniels
Download Presentation

Area and Perimeter: Areas of Regular Polygons

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. Area and Perimeter:Areas of Regular Polygons

  2. inscribed polygon circumscribed circle Review: Inscribed Polygons & Circumscribed Circles Inscribed means writteninside Circumscribed means writtenaround (the outside) Def: A polygon is inscribed in a circle & the circle is circumscribed about the polygon when each vertex of the polygon lies on the circle. Def:A ________________is a polygon that is equiangular & equilateral.

  3. Inscribed Regular Polygons & Triangles Inscribed Regular Pentagon Total of Interior Angles = ___________ Each Interior Angle = ______________ 5 congruent isosceles triangles Total of Central Angles = _________ Each central angle = _____________

  4. Parts of a Regular Polygon • A stands for Area • A(nonagon) is the area of a regular 9-sided figure. • n is the number of sides of a regular polygon • p is perimeter, r is radius, s is side • a is apothem • ____________ – The line segment from the center of a regular polygon to the midpoint of a side or the length of this segment. • Sometimes known as the ______________, or the radius of a regular polygon’s inscribed circle.

  5. O a s Y X Regular Polygon Area Theorem Given: an inscribed regular n-gon (shown as an octagon) A(n-gon) = Regular Polygon Area Theorem: The area of a regular polygon is ___________________________________________ ____________________________________________________

  6. O (Regular Octagon) M Y X Regular Polygon Terminology _______________________- the center of the circumscribed circle (O). _______________________- the distance from the center to a vertex (OX). _____________________________- an angle formed by 2 radii drawn to consecutive vertices. ( ) ____________________________- the (perpendicular) distance from the center of the polygon to a side. (OM)

  7. r = . Find a, p, A. r a 45 x s Example: Square

  8. a = 4. Find r, p, A . r a 30 x s Example: Equilateral Triangle

  9. a = . Find r, p, A. r a 60 x s Example: Regular Hexagon

  10. r = 10; Find a, p, A. a r x X s 70 Regular Nonagon

  11. Examples r r a a

  12. More Examples s r r r a a a x x x 1.r = , find A. 2.a = 6, find A. 3.a = 8, find p. 4.r = 12, find s. 5.s = 8, find r.

More Related