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Section 11.1

Areas of Regular PolygonsSection 11.2

Theorem 11.3 Area of an Equilateral Triangle: The area of an EQUILATERAL triangle is one fourth the square of the length of the side times .

where A represents the area and s represents the side length of the triangle.

Example 1: Find area of the triangle.10Example 2: If the area of an equilateral triangle is 26cm2, find the length of each side.

Other Regular Polygons:Center of Polygon: where diagonals intersect.

Central angle of a polygon: an angle whose vertex is the center of the polygon and whose sides contain two consecutive vertices of the polygon:

Radius: the distance from center to vertex (corner)

Apothem: the distance from the center of a polygon to any side.

Theorem 11.4: Area of a Regular Polygon: The area of a REGULAR n-gon, with side length s is half the product of the apothem a and the perimeter P, so

where A represents the area a represents the apothem of the n-gon and P represents the perimeter of the n-gon.

Example 3: A regular pentagon with radius 4. Find the area of the pentagon.a) What type of shape is this? _____________________b) What is the central angle? _____________________ What is the top angle in the triangle? ________________c) What is the apothem? _____________________d) What is half the side length of the polygon? ___________e) What is the whole side length of the polygon? __________f) What is the perimeter of the polygon? _______________g) Find the Area. __________________Example 4: A regular hexagon is inscribed in a circle with apothem 5. Find the area of the hexagon.a) What type of shape is this? _____________________b) What is the central angle? _____________________ What is the top angle in the triangle? ________________c) What is the apothem? _____________________d) What is half the side length of the polygon? ___________e) What is the whole side length of the polygon? __________f) What is the perimeter of the polygon? _______________g) Find the Area. __________________


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