10-5: Areas of Regular Polygons Every regular polygon has a center C ENTER : A point on the interior that is equidistant from all the vertices A POTHEM.

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Presentation transcript:

10-5: Areas of Regular Polygons Every regular polygon has a center C ENTER : A point on the interior that is equidistant from all the vertices A POTHEM : A segment drawn from the center that is perpendicular to a side of a regular polygon

10-5: Areas of Regular Polygons Area of a regular polygon: A = ½aP, where a = an apothem P = the perimeter P a

10-5: Areas of Regular Polygons The game board below has a hexagon-shaped board. Find its area. First, find the perimeter P = 9 in  6 sides = 54 in. A = ½aP = ½(7.8)(54) = in 2 Your Turn Each of the tiles is also a regular hexagon. Find the area of a tile if the sides are 0.9 in long and each apothem is 0.8 in long in 2

Find the area of the shaded region in the regular polygon to the right This is simply a regular polygon, with a triangle cut out. A shaded = A whole – A cut Whole perimeter = 5(8) = 40 ft Whole area = ½(40)(5.5) = 110 ft2 Cut area (triangle) = ½(8)(5.5) = 22 ft 2 A shaded = 110 – 22 = 88ft 2

Find the area of the shaded region for the regular polygon below m 2

Assignment Worksheet #10-5 Note: For #7 & 8, I want you to find the area of the unshaded region