Section 11.6: Areas of Regular Polygons Definitions – Given a regular polygon inscribed in a circle, the center and radius of the polygon is the center.

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Presentation transcript:

Section 11.6: Areas of Regular Polygons Definitions – Given a regular polygon inscribed in a circle, the center and radius of the polygon is the center and radius of the circle.

A central angle of a regular polygon is an angle formed by two radii drawn to consecutive vertices of the polygon. To find the measure of each central angle, divide 360  by the number of sides.

Example 1: Find the central angle of a regular pentagon.

Example 2: Use the central angle of the regular pentagon to find the length of the apothem if a side of the polygon is 8 cm.

Example 2 continued: Since AB = 8 cm, then AG = 4 cm. Now use trig to solve for the apothem FG. So the apothem, FG, is approximately 5.5 cm.

Example 3: Find the length of the apothem of a regular hexagon of side length 10 in, and then find the hexagon’s area.

Example 4: Use theorem to find the area of a regular hexagon with side 10 cm.

Example 5: Use theorem to find the area of a regular octagon with side 10 cm. What about with a radius of 10cm?