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9.4 Areas of Regular Polygons
February 6, 2008
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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.
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The center of circle A is: A The center of pentagon BCDEF is:
A radius of circle A is: AF A radius of pentagon BCDEF is: An apothem of pentagon BCDEF is: AG B F C A G E D
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Area of a regular polygon
The area of a regular polygon is: A = ½ Pa Area Perimeter apothem
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Where does the equation come from?
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
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Ex 1: A regular octagon has an apothem. of 4 in. Side length is 3
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)
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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 Find the area of the pentagon. C B D A
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