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Area and Perimeter: Areas of Regular Polygons

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

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Area and Perimeter: Areas of Regular Polygons

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  1. Area and Perimeter:Areas of Regular Polygons Keystone Geometry

  2. inscribed polygon circumscribed circle Review: Inscribed & Circumscribed with Polygons and 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 regular polygon is a polygon that is equiangular & equilateral.

  3. Inscribed Regular Polygons & Triangles Inscribed Regular Pentagon Total of Interior Angles = 540 Each Interior Angle = 108 5 congruent isosceles triangles Total of Central Angles = 360 Each central angle = 72

  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 • 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 inradius, or the radius of a regular polygon’s inscribed circle.

  5. O a s Y X where, p = the perimeter 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 one half the product of the apothem & the perimeter.

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

  7. a = 4. Find r, p, A . r a 30 x s Example: Equilateral (regular) Triangle

  8. r = . Find a, p, A. r a 45 x s Example: Square (regular Quadrilateral)

  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.

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