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Areas of Regular Polygons

Areas of Regular Polygons. Section 11.3. Regular polygon – all sides congruent all angles congruent Hexagon BDEFGH is a regular hexagon inscribed in circle A. and are radii that create an isosceles triangle Height of is is called an apothem of the hexagon

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Areas of Regular Polygons

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  1. Areas of Regular Polygons Section 11.3

  2. Regular polygon – all sides congruent all angles congruent • Hexagon BDEFGH is a regular hexagon inscribed in circle A

  3. and are radii that create an isosceles triangle • Height of is • is called an • apothem of the hexagon • An apothem is a segment • drawn from the center of a regular polygon perpendicular to the side

  4. If side is labeled s, then the area of • is A = ½ bh or substitute s for b and a (apothem) for h • There are 6 triangles in the hexagon so to find the area of the hexagon it would be

  5. The perimeter, P, of the hexagon is 6s so we can replace the 6s in the formula with P.

  6. The formula A = ½ aP can be used for any regular polygon. • Ex. 1 Find the area of a regular pentagon with a perimeter of 90 meters. Round to nearest tenth.

  7. Ex. 2 Find the area of a regular octagon with a perimeter of 124 inches. Round to nearest tenth.

  8. Ex. 3 Find the area of a square with apothem length of 2.5 meters.

  9. Ex. 4 Find the area of a regular hexagon with an apothem length of 18 inches.

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