of sides of triangles Sum of measures of
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# of sides # of triangles Sum of measures of interior angles 3 1 1(180)=180 4 2 2(180)=360 5 3 3(180)=540 6 4 4(180)=720 n n-2 (n-2) • 180
If a convex polygon has n sides, then the sum of the measure of the interior angles is (n – 2)(180°)
If a regular convex polygon has n sides, then the measure of one of the interior angles is
Ex. 1 Use a regular 15 -gon to answer the questions. A) Find the sum of the measures of the interior angles. 2340° B) Find the measure of ONE interior angle 156°
Ex: 2 Find the value of x in the polygon x 126 100 143 130 117 126 + 130 + 117 + 143 + 100 + x = 720 616 + x = 720 x = 104
Ex: 3 The measure of each interior angle is 150°, how many sides does the regular polygon have? One interior angle A regular dodecagon
Two more important terms Interior Angles Exterior Angles
The sum of the measures of the exterior angles of a convex polygon, one at each vertex, is 360°. 2 1 3 5 4
The sum of the measures of the exterior angles of a convex polygon, one at each vertex, is 360°. 1 3 2
The sum of the measures of the exterior angles of a convex polygon, one at each vertex, is 360°. 1 2 4 3
The measure of each exterior angle of a regular polygon is
Ex. 4 Find the measure of ONE exterior angle of a regular 20 -gon. 18°
Ex. 5 Find the measure of ONE exterior angle of a regular heptagon. 51. 4°
Ex. 6 The sum of the measures of five interior angles of a hexagon is 625. What is the measure of the sixth angle? 95°
Let’s practice! 11. 1 Worksheet
Area of an Equilateral Triangle 30 30 s s 60 60 s
Ex: 1 Find the area of an equilateral triangle with 4 ft sides.
A Circle can be circumscribed around any regular polygon
VERTICES
A Central Angle is an whose vertex A RADIUS joins theangle center of the is the polygon center and two regular withwhose any ofsides the are vertices consecutive radii
A Regular Hexagon Equal Sides Equal Angles s How many equilateral triangles make up a regular Hexagon? What is the area of each triangle? What is the area of the hexagon? 6 • (the area of the triangle)
41. 569 What is the area of this regular hexagon? units 2 4 The area of an equilateral triangle A = 6. 9282 The area of our equilateral triangle in this example How many identical equilateral triangles do we have? 6 A = 6 * (6. 9282) The area of our hexagon in this example
An APOTHEM is the distance between the center and a side. (It MUST be perpendicular to the side. )
How to find the You need to know the apothem and perimeter Area = (1/2) • a • P or A =. 5 • a • P
Area of a Regular Polygon: A = ½ a. P A =. 5 (apothem) (# of sides)(length of each side) a
A Regular Octagon 7 ft
360/8=45 22. 5° 45 x 7 3. 5 ft
Perimeter is 56 feet Apothem is 8. 45 feet 7 ft What is the area? Area =. 5 • 8. 45 • 56 Area = 236. 6 2 ft
11. 2 Worksheet Practice B ODDS
Worksheets’ EVENS
