lesson 10.2.notebook
April 14, 2016
Warm Up #2
1) Find the Area and Circumference of the circle.
d = 8 in
C = ______
A = ______
2) Find the area of the triangle to the nearest tenth.
A = ______
5 in.
30o
3) Find the lower base of the trapezoid if Area = 70 in2, h=7 in, and upper base=5in.
5 in.
7 in.
x
lesson 10.2.notebook
April 14, 2016
lesson 10.2.notebook
April 14, 2016
lesson 10.2.notebook
April 14, 2016
lesson 10.2.notebook
April 14, 2016
lesson 10.2.notebook
April 14, 2016
lesson 10.2.notebook
April 14, 2016
10.2 GOALS
1) Develop and apply the formulas for the area and circumference of a circle.
2) Develop and apply the formula for the area of a regular polygon.
lesson 10.2.notebook
April 14, 2016
Vocabulary
circle
center of a circle
center of a regular polygon
apothem
central angle of a regular polygon
lesson 10.2.notebook
April 14, 2016
A circle is named by the symbol ¤ and its center ¤A
C = dπ or C = 2rπ
A = r2π
radius AB, AD, AC diameter CD diameter d = CD
lesson 10.2.notebook
April 14, 2016
2 ways to provide answers
d=6 in
In terms of pi
rounded to the nearest tenth
lesson 10.2.notebook
April 14, 2016
Finding Measurements of Circles
1) Find the area of ¤K in terms of π.
2) Find the radius of ¤J if the circumference is (100π )m.
3) Find the circumference of ¤M if the area is (25π)ft2
lesson 10.2.notebook
April 14, 2016
4) Find the area of ¤A in terms of π in which C = (4π) m.
lesson 10.2.notebook
April 14, 2016
Vocabulary for a regular polygon
Center of a regular polygon
Radius
Apothem
Central Angle
lesson 10.2.notebook
April 14, 2016
The center of a regular polygon is equidistant from the vertices. Q
lesson 10.2.notebook
April 14, 2016
The apothem is the distance from the center to a side
a
Q
lesson 10.2.notebook
April 14, 2016
A central angle of a regular polygon has its vertex at the center, and its sides pass through consecutive vertices
Q
Each central angle measure of a regular n­gon is lesson 10.2.notebook
April 14, 2016
What is the value of one central angle of each regular polygon?
3 sides
6 sides
4 sides
7­sides
5 sides
8 sides
lesson 10.2.notebook
Name each:
1) ∠FGH ____
2) ∠GCH ____
3) point C ____
4) segment BC ____
5) segment CF ____
April 14, 2016
Regular pentagon DEFGH lesson 10.2.notebook
April 14, 2016
Identify the red part of each regular polygon
_______
_________
_________
_________
lesson 10.2.notebook
April 14, 2016
lesson 10.2.notebook
April 14, 2016
lesson 10.2.notebook
April 14, 2016
The apothem always cuts the central angle in half.
The apothem always cuts the side of the polygon in half.
lesson 10.2.notebook
April 14, 2016
lesson 10.2.notebook
30o 30o
April 14, 2016
25.7o 25.7o
6 in
6 in
6
36o 36o
6 in
lesson 10.2.notebook
April 14, 2016
Three types of problems
1) given the side of the polygon The side of a hexagon is 6 in.
30o 30o
6 in
6 in
lesson 10.2.notebook
April 14, 2016
Three types of problems
2) given the radius of the polygon The radius of a hexagon is 6 in.
30o 30o
6 in
6 in
lesson 10.2.notebook
April 14, 2016
Three types of problems
3) given the apothem of the polygon The apothem of a hexagon is 6 in.
30o 30o
6 in
6 in
lesson 10.2.notebook
April 14, 2016
Finding the Area of a Regular Polygon
Find the area of regular heptagon with side length 2 ft to the nearest tenth.
Step 1 Draw the heptagon. The central angle is _____. 2 ft.
51.4o
Step 2 Draw the triangle formed by the central angle. Draw the apothem, which bisects the central angle and the side of the polygon to form a right triangle. 51.4o
2 ft.
lesson 10.2.notebook
April 14, 2016
Step 3 Use the tangent ratio to find the apothem.
51.4o
2 ft.
51.4o
2 ft
lesson 10.2.notebook
April 14, 2016
Step 4 Use the apothem and the given side length to find the area.
lesson 10.2.notebook
April 14, 2016
Your Turn #1
Find the area of a regular dodecagon with side length 5 cm to the nearest tenth.
Step 1 Draw the dodecagon. The central angle is_____. Step 2 Draw the triangle formed by the central angle. Draw the apothem, which bisects the central angle and the side of the polygon to form a right triangle. Step 3 Use the tangent ratio to find the apothem. Step 4 Use the apothem and the given side length to find the area.
lesson 10.2.notebook
April 14, 2016
Find the area of a regular dodecagon with side length 5 cm to the nearest tenth.
5 cm
lesson 10.2.notebook
April 14, 2016
Your Turn #2
Find the area of a regular octagon with a side length of 4 cm.
Step 1 Draw the octagon. The central angle is_____. Step 2 Draw the triangle formed by the central angle. Draw the apothem, which bisects the central angle and the side of the polygon to form a right triangle. Step 3 Use the tangent ratio to find the apothem. Step 4 Use the apothem and the given side length to find the area.
lesson 10.2.notebook
April 14, 2016
Find the area of a regular octagon with a side length of 4 cm.
4 cm
lesson 10.2.notebook
April 14, 2016
Your Turn #3
Find the area of the regular hexagon that has a distance of 15 inches from the center to the vertices. 15 in.
lesson 10.2.notebook
April 14, 2016
Your Turn #4
A regular triangle with an apothem of 10 inches. Find the area of the triangle.
10 lesson 10.2.notebook
April 14, 2016
10.2 Classwork: Worksheet
lesson 10.2.notebook
April 14, 2016
lesson 10.2.notebook
April 14, 2016
lesson 10.2.notebook
April 14, 2016
lesson 10.2.notebook
April 14, 2016
10.2 homework pg 691 #4, 6­9, 18­25, 30 Short quiz Thursday/Friday (4 problems)
1) Rhombus/Kite
2) Trapezoid
3) Circle
4) Regular Polygon
lesson 10.2.notebook
April 14, 2016
lesson 10.2.notebook
April 14, 2016