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9.4 Areas of Regular Polygons

9.4 Areas of Regular Polygons. February 6, 2008. Definitions (associated with regular polygons only). Center of a polygon – the center of its circumscribed circle. Radius of a polygon – the radius of its circumscribed circle, or the distance from the center to a vertex.

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9.4 Areas of Regular Polygons

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  1. 9.4 Areas of Regular Polygons February 6, 2008

  2. Definitions (associated with regular polygons only) Center of a polygon – the center of its circumscribed circle. Radius of a polygon – the radius of its circumscribed circle, or the distance from the center to a vertex. Apothem of a polygon – distance from the center to any side of the polygon.

  3. B The center of circle A is: A The center of pentagon BCDEF is: A A radius of circle A is: AF A radius of pentagon BCDEF is: AF An apothem of pentagon BCDEF is: AG F C A G E D

  4. Area of a regular polygon The area of a regular polygon is: A = ½ Pa Area Perimeter apothem

  5. Where does the equation come from? F • The apothem is the height of a triangle between the center and two consecutive vertices of the polygon. • you can find the area o any regular n-gon by dividing the polygon into congruent triangles. A H a E G B D C Hexagon ABCDEF with center G, radius GA, and apothem GH

  6. Ex 1: A regular octagon has an apothem of 4 in. Side length is 3. Find its area. Step 1: Find Perimeter 3 x 8 = 24 Step 2: Use Equation a 4 A = ½ Pa = ½ (24)(4)

  7. Ex: A regular octagon has a radius of 8.2 in. Find its area. 67.5o x 8.2

  8. Ex. 2: Finding the area of a regular polygon • A regular pentagon is inscribed in a circle with a side length of 7.5 and an apothem of 5.2. Find the area of the pentagon. C B D A

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