Geometry 11.6 Big Idea: Find Areas of Regular Polygons

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Presentation transcript:

Geometry 11.6 Big Idea: Find Areas of Regular Polygons

Regular polygon: a polygon with all angles and all sides congruent Reminders: Inscribed polygon: polygon drawn in the interior of a circle where all vertices lie on the circle Regular polygon: a polygon with all angles and all sides congruent

The center of the polygon and the radius of the polygon are the center and the radius of its circumscribed circle.

Apothem of the polygon: Vocabulary: Apothem of the polygon: Perpendicular distance from the center of the regular polygon to any side of the polygon

Vocabulary: Central angle of a regular polygon: angle formed by two radii drawn to consecutive vertices of the polygon

Measure of Each Central Angle of a Regular Polygon To find the measure of each central angle of a regular polygon, divide 360° by the number of sides, n.

Example: Find each angle measure in ABCDE.

Theorem 11.11: Area of a Regular Polygon Area of a regular n-gon is ½ the product of the apothem a and the perimeter P.

Example: Find the perimeter and area of the regular polygon.

Example: Find the perimeter and area of the regular polygon.