Transcript Ratios of Area

Ratios of Area of
2D Shapes
Geometry
Objective
• Find the ratio of the area
and perimeters of similar
shapes while applying the
relationships between scale
factors, perimeters, and
areas of those shapes
What is a Ratio??
• A ratio is the comparison
of two objects.
• A Scale Factor is the ratio
of any two corresponding
lengths in two similar
geometric figures.
Example
8 ft
5 ft
Width of Car
Width of model
=
Length of Car
Length of model
=
5 feet
5 inches
= 1 : 1 ???
5 in
8 in
Ratios of Triangles
If two triangles have equal
heights, then the ratio of
their areas equal the ratio
of their bases
Ratio of Areas = Ratio of Bases
Height
Area of Triangle A
A
8
8
=
Area of Triangle B
3
B
3
Scale Factor
Titanic Example
• MODEL BUILDING. A scale model of the
Titanic is 107.5 inches long and 11.25 inches
wide. The Titanic itself was 882.75 feet long.
How wide was it?
Width of Titanic
Width of model
=
Length of Titanic
Length of model
LABELS:
Width of Titanic = x
Width of model ship = 11.25 in
Length of Titanic = 882.75 feet
Length of model ship = 107.5 in.
Reasoning:
Width of Titanic
Length of Titanic
=
Width of model
Length of model
X feet
11.25 in.
=
882.75 feet
107.5 in.
x = 11.25 in.(882.75 feet)
107.5 in.
x ≈ 92.4 feet
Ratios of Triangles
• If two triangles have equal
bases, then the ratio of
their areas equals the
ratio of their heights
Area of Triangle A
A
5
9
Area of Triangle B
=
9
5
B
Scale Factor
Ratios of Triangles
• If two triangles are
similar, then the ratio of
their areas equals the
square of their scale
factor
3
Area of Triangle A
= 6
6
Area of Triangle B
A
1
B
3
=
4
( )
2
Scale Factor of Similar
Figures
If the scale factor of two
similar figures is a:b. then
1) The ratio of the
2:1
perimeters is a:b
2)The ratio of the areas
4:1
is a :b
2
2
2
A
1 B
Scale Factor Example
Find the area and perimeter of
two similar figures with a scale
factor of 3:5.
a:b = 3:5
3
Ratio of perimeters
= a:b = 3:5
Ratio of area
2
2
= a :b = 9:25
5
Scale Factor Example
The ratio of the areas of two
similar figures is 1:4. Find
the ratio of their
perimeters.
Area a= 1
Ratio of area =
:
= 1:4
so a:b = 1:2
Area b= 4
Ratio of perimeters =a:b 1:2