11.1 Areas of Polygons

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11.1 Areas of Polygons
2
Area of a Square _______________________ Area
of a Rectangel ____________________ Postulate
18 ___________________________ _________________
______________________
3

• If we are finding the area of a shape we do not
  know
• __________________________________
• __________________________________
• __________________________________

2
3
4
2
10
4
Classify as True or False
5
Examples
14
60
30
Find the Area of the square.
Find the Area of the rectangle.
6
11.3 Areas of ParallelogramsTriangles and
Rhombuses
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Formulas
Area of a Parallelogram ________________ Area
of a Triangle ____________________ Area of a
Rhombus __________________
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Hint file this one away. ______________________
____________ __________________________________ __
________________________________
Examples Find the Area 1. Rhombus with
Diagonals of 6 8. 2. Triangle with a base of
6 and height of 10.
9
3. Rhombus with a Perimeter of 52 and a diagonal
of 24. 4. Parallelogram with sides of 10 and
20
12
24
10
45
20
10
5. Find the area of an isosceles triangle with
congruent sides of 4 and a base of 2.
4
4
2
11
8
10
Find the Area
12
135
5
Find the Area
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11.3 Areas of Trapezoids
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What was a Trapezoid? ___________________________
___ What was the median? ________________________
______ Area Trapezoid ____________________ _____
_____________________________
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Examples
10
8
60
15
16
A trapezoid has an area of 75 and a height of 5.
How long is the median?
Which formula?
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Examples
8
8
8
60
18
2
45
Find the Area
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Examples
18
30
30
30
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11.4 Areas of REGULAR Polygons
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Think of all REGULAR polygons as being inscribed
in a circle.
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Definitions Center ___________________________
___ Radius _____________________________ _____
________________________________ Central Angle
_______________________ Central Angle
_______________________ __________________________
___________
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Area of Regular Polygon _____________ ___________
________________________ What Shapes can we use
this for? _______________________________________
__________________________________________________
___________________
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Finding the Central Angle is important because in
some polygons it will form special triangles with
the Radius and Apothem (ie 45-45-90 or 30-60-90)
Central Angle _______________________
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CA______ CA_____ CA______
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Examples
1. Find the Area of a Regular hexagon with an
apothem of 6.
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r a P A
1)
2)
Complete the Chart for a Square
45
r
a
45
½ side
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Complete the Chart for a Triangle
r a P A
1)
2)
Complete the Chart for a Hexagon
r a P A
1)
2)
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11.5 Circumference and Areas of Circles
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Formulas
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Examples
1. The radius of circle A is 3 times the radius
of circle B. Compare the circumferences of
circle A to circle B.
2. Now compare the Areas of A to B
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Fill out the Chart for circle M.
r D C A
1)
2)
3)
4)
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1. The diameter of the worlds largest circle is
   16m. Find the circumferences of the crust.

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11.6 Arc lengths andAreas of Sectors
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Sector _____________________________ ___________
_________________________
__________________________________ _______________
___________________
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Formulas
A
B
O
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• The radius of a circle is 3, and the central
  angle is 50.
• Find the length of the arc
• Find the area of the sector

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1. The area of a sector of a circle is and
   the central angle is 9 degrees. Find the radius
   of the circle

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Find the area of the shaded region
120
6
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11.7 Ratios of Areas
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We will be comparing areas of figures by
comparing ratios
Case 1
B
A
C
D
x
z
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We will be comparing areas of figures by
comparing ratios
Case 2
B
D
h
k
A
C
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Case 3 If triangles are similar
then ______________________________________

• Recap
• If heights the same then
• ___________________________________
• 2. If Bases the same then
• ___________________________________
• 3. If Triangles are similar then
• ___________________________________

44
Examples
B
Compare the Ratios of areas between
6
A
D
C
3
12
45
If the scale factor of 2 similar figures is ab
then 1. the ratio of the perimeters
is_______ 2. The ratio of the areas is_______
If the scale factor of 2 similar figures is 35
then 1. the ratio of the perimeters
is_______ 2. The ratio of the areas is_______
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1. The diameters of 2 circles is 10 and 9. What
is the ratio of their circumferences and Areas?
Ratio of Circumferences_______ Ratio of
Areas_______________
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2. A pentagon with sides of 5,7,8,9 and 11 has
an Area of 96. Find the perimeter of a similar
pentagon whose Area is 24.