Chapter 11 Areas of Polygons and Circles Section 11.2 Area of Regular Polygons Find the area of an equilateral triangle Find the area of a regular polygon

Example 1 Area Equilateral Triangle Example 2 Area Regular Pentagon Example 3 Area Regular Octagon Example 4 Always, Sometimes, Or Never CA Standard 12.0 Students find and use measures of sides and of interior and exterior angles of triangles and polygons to classify figures and solve problems. (Key) Lesson 1 Contents

Find the area of an equilateral triangle 30° 60° 60°

Find the area of an equilateral triangle

Find the area of the triangle Find the area of an equilateral triangle Find the area of the triangle The Triangle is equilateral with s = 11 Area Equilateral  s = 11 Simplify Answer: The triangle has area of square units Example 1-1a

Find the area of the triangle Find the area of an equilateral triangle Find the area of the triangle Answer: The triangle has area of square units You 1

Center of circumscribed circle Radius of circumscribed circle Vertex is on the center, Sides connect consecutive vertices Distance from center to any side of the polygons

To find the area of the hexagon, find the area of one triangle and multiply by 6 Height of the triangle is an apothem of the hexagon Base of the triangle is a side of the hexagon 6 is the number of sides of the hexagon h b

Perimeter = ns = 5(5) = 25 units Find the area of a regular polygon 5 4 Perimeter = ns = 5(5) = 25 units

Need to find the apothem and side length Find the area of a regular polygon Need to find the apothem and side length Apothem = BD Side Length = AC Look at ABC Example 1-3a

Find BD and AC BD = cos 36 AC = 2 sin 36 Find the area of a regular polygon Find BD and AC BD = cos 36 AC = 2 sin 36 Example 1-3b

Apothem = BD = cos 36 s = AC = 2(DC) = 2 sin 36 Find the area of a regular polygon Apothem = BD = cos 36 s = AC = 2(DC) = 2 sin 36 Example 1-3c

Find the area of an octagon with radius 3 cm Find the area of a regular polygon Find the area of an octagon with radius 3 cm Need to find the apothem and side length This angle is half the Central Angle 45  2 = 22.5 Central Angle has measure 360  8 = 45 This length is half of s a s Example 1-2a

Find the area of an octagon with radius 3 cm Find the area of a regular polygon Find the area of an octagon with radius 3 cm Need to find a and s using the triangle a 22.5° s = 6 sin 22.5 Example 1-2a

Find the area of an octagon with radius 3 cm Find the area of a regular polygon Find the area of an octagon with radius 3 cm s = 6 sin 22.5 a s Example 1-2a

Find the Area and Perimeter of the following pentagon Find the measures of interior and exterior angles of polygons Find the Area and Perimeter of the following pentagon Answer: Area = 1125 tan 36  817.4 Square Units Perimeter = 150 tan 36  109 Units You 2

Always Always Example 1-4a

HW # 48 Pg 672-675 9-29, 30-52