½ bh where b is the base and a is the altitude perpendicular to that base

The endpoints of a radius are the what?

the center and a vertex of the polygon.

Since the radii are all the same and each radius is a side of a triangle in the regular polygon, then?

The two consecutive radii are the legs of an isosceles triangle.

Every n-gon can be divided into what?

n congruent isosceles triangles. (n = number of sides)

The area of any regular polygon is what?

n times the area of one of those isosceles triangles.

The apothem of a regular polygon is the same as what?

The same as the altitude as the isosceles triangle.

The endpoints of the apothem are what?

The center of the polygon and the midpoint of a side.

(Area of any Regular Polygon) The base b of the triangle is what?

the same as the side s of the polygon.

The height h of the triangle is what?

the same as the apothem a of the polygon.

n ∙ (area of the isosceles triangle) or n ∙ ( ½ b ∙ h) or n ∙ ( ½ s ∙ a) or ½ a ∙ ns or ½ a ∙ P where P is the Perimeter of the polygon

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Geom Lession 11.2

Lesson 11.2 Extra Notes on the Areas of Regular Polygons

Question	Answer
Area of a triangle =	½ bh where b is the base and a is the altitude perpendicular to that base
The radius of a polygon is the same as the radius a what?	circle
The endpoints of a radius are the what?	the center and a vertex of the polygon.
Every radius in the same polygon or circle is	congruent
Since the radii are all the same and each radius is a side of a triangle in the regular polygon, then?	The two consecutive radii are the legs of an isosceles triangle.
Every n-gon can be divided into what?	n congruent isosceles triangles. (n = number of sides)
The area of any regular polygon is what?	n times the area of one of those isosceles triangles.
The apothem of a regular polygon is the same as what?	The same as the altitude as the isosceles triangle.
The endpoints of the apothem are what?	The center of the polygon and the midpoint of a side.
Area of a regular polygon =	n(area of a triangle)
where n =	number of sides
(Area of any Regular Polygon) The base b of the triangle is what?	the same as the side s of the polygon.
The height h of the triangle is what?	the same as the apothem a of the polygon.
A = ?	n ∙ (area of the isosceles triangle) or n ∙ ( ½ b ∙ h) or n ∙ ( ½ s ∙ a) or ½ a ∙ ns or ½ a ∙ P where P is the Perimeter of the polygon

Created by: marcrobertdillon

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