Download Geometry - Semester 2

Geometry - Semester 2
Mrs. Day-Blattner
3/4/2016 Unit 3 Lesson 10
Agenda 3/4/2016
1. Unit 3 Lesson 10 Finding the Perimeter and Area of
Regular Polygons
2. Lesson 11- From the area of a polygon to the area of a
circle. Do calculations to complete table in question 2 on
page 70.
3. Draw a circle and cut it into small segments of equal size.
4. Homework
Lesson 10: Finding the Perimeter and Area of Regular
Polygons
Important Vocabulary (page 65)
1) polygon
any region enclosed by line segments (a plane shape with
straight sides)
smallest polygon would be a triangle
Useful Non-example circle
Lesson 10: Finding the Perimeter and Area of Regular
Polygons
2) Interior angle of a polygon is an
angle made by adjacent sides of a
polygon
Lesson 10: Finding the Perimeter and Area of Regular
Polygons
Important Vocabulary (page 65)
3) perimeter - the sum of the lengths of the edges of a polygon
Example
Perimeter = 30cm
Non-Example?
7.4 Planning the Gazebo
What Zac thinks he knows: Do you agree or disagree?
Explain why?
Two radii drawn to two
consecutive vertices of the
regular hexagon form a
central angle whose
measure can be found
based on the rotational
symmetry of the figure.
7.4 Planning the Gazebo
What Zac thinks he knows: Do you agree or disagree?
Explain why?
The hexagon can be
decomposed into 6
congruent isosceles
triangles.
7.4 Planning the Gazebo
What Zac thinks he knows: Do you agree or disagree?
Explain why?
The length of the altitudes
of each of these 6
congruent triangles (the
altitude drawn from the
vertex of the triangle which
is located at the center of
the circle) can be found
using trigonometry.
7.4 Planning the Gazebo
What Zac thinks he knows: Do you agree or disagree?
Explain why?
The length of the altitudes
sin(60degree) =
of each of these 6
congruent triangles (the
altitude / radius
altitude drawn from the
vertex of the triangle which
or altitude = r(sin60)
is located at the center of
the circle) can be found
using trigonometry.
7.4 Planning the Gazebo
What Zac thinks he knows: Do you agree or disagree?
Explain why?
The length of the sides of
each the triangles that form
the chords of the circle can
be found using
trigonometry.
cos60degrees = ½
side/radius
rcos60 = ½ side
or 2rcos60 = side
2. Based on what you and Zac know, find the
perimeter of the hexagon that he inscribed in the circle
with a radius of 2 inches. Illustrate and describe your
strategy so someone else can follow it.
1 side = 2 (2in)cos60 degrees = 4in(½) = 2 in
Perimeter = 6 x side length = 6 x 2in = 12 in.
3. Now find the area of the hexagon that Zac inscribed
in the circle with a radius of 2 inches. Illustrate and
describe your strategy so someone else can follow it.
Altitude = 2in(sin60deg) = 1.73 in
Area of one of isosceles triangles = ½ base x altitude
= ½ (2in) (1.73in) = 1.73 in2
Area of hexagon =6 x 1.73 in2 = 10. 38 in2
4. and 5 Modifying the shapes inscribed in the circle.
Ready, Set, Go! Radius and Area or circumference.
1. Radius = 1m
Area = πm2
Circumference = 2πm
Ready, Set, Go! Radius and Area or circumference.
2. Radius = 3ft
(sq.rt of 9)
Area = 9πft2
Circumference = 6πft
(d = 2x3ft)
Ready, Set, Go! Radius and Area or circumference.
3. Radius = 4yd
Area = 16πyd2
Circumference = 8πyd
(r = ½ 8 )
Ready, Set, Go! Radius and Area or circumference.
4. Radius = 1m
Area = 3.14m2
(π = 3.14, r x r = 1)
Circumference = 2πm
(d = 2 x r )
Ready, Set, Go! Radius and Area or circumference.
5. Radius = 7 miles
Area = 49πmiles2
Circumference = 14π miles
Ready, Set, Go! Radius and Area or circumference.
6. Radius = 9 in
(sq. rt 81 = 9)
Area = 81πin2
Circumference = 18π in
Set : Finding area and perimeter of regular polygons
7. - 10 Document camera.
Lesson 11. (7.5) From polygons to circles
Homework.
Cut up your circle into equal segments and bring them back to class on Tuesday
in an envelope or plastic bag.
Pages 73-74 Questions 7, 8, 9 and 10.