#### 11.7 Ratio of Areas

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11.7 Ratio of Areas

Geometry
11.7
Ratio of Areas
Comparing Areas of Triangles
If two triangles have equal heights, then the ratio of
their areas equals the ratio of their bases.
A = ½(10)(12) = 60
12
10
Ratio of bases:
10 = 1
20
2
A = ½(20)(12) = 120
12
20
Ratio of areas:
60 = 1
120
2
Comparing Areas of Triangles
If two triangles have equal bases, then the ratio of
their areas equals the ratio of their heights.
A = ½(20)(15) = 150
15
10
20
Ratio of heights:
15
10
A = ½(20)(10) = 100
20
3
=
2
Ratio of areas:
150 = 3
100
2
Comparing Areas of Triangles
If two triangles are similar, then the ratio of their
areas equals the square of their scale factor.
P = 12 + 16 + 20 = 48
P = 6 + 8 + 10 = 24
A = ½(12)(16) = 96
20
16
A = ½(6)(8) = 24
10
8
6
12
48
2
Scale Factor:
=
=
= Ratio of Perimeters 24
1
Ratio of areas:
96
24
4
=
1
=
2
1
2
What to ask yourself!!!
1) Do the triangles have the same height?
– If yes, the ratio of the areas is the ratio of the bases.
2) Do the triangles have the same base?
– If yes, the ratio of the areas is the ratio of the heights.
3) Are the figures similar?
– If yes, the ratio of the areas is the square of the scale
factor.
Exercises
same height
A
B
3
C
9
S
= 3:12
= 1:4
1. ∆ABC to ∆ABD
= 7:2
O
7
S
3. ∆GEO to ∆SEO
= 5:6
same base
G
E
5 O 6
2
2. ∆SEO to ∆GEO
same height
G
same base
G
E
D
5
R
6
E
S
4. ∆GES to ∆RES
= 7:6
Exercises
Scale Factor
Ratio of Perims
Ratio of
a
b
a
b
a
Areas
b
2
1.
2.
3.
4.
3:4
5:9
(6:9)
2:3
5x : 2y
3:4
5:9
(6:9)
5x:2y
2:3
9:16 25:81
36 : 81
5.
6.
7.
3x:2z 4x:7y
(3√2)x:
(2√7)y
4x:7y
(3√2)x:
(2√7)y
3x:2z
25x²:4y²
16x2:49y2
9x²:4z²
18x2:28y2
Exercises
8.
Two circles have areas 49π
and 64π. What is the ratio of
the diameters and of the
circumferences?
9.
The lengths of two
similar hexagons are
x2 : x4y4
What is the ratio of their
areas?
r=7
Scale Factor:
r=8
All circles are similar.
Ratio of diameters
and circumference is
the ratio of their
radii.
7:8
Ratio of areas:
x2
1
= 2 4
4 4
x y
x y
2
1
2 4
x y
1
4 8
x y
One from the HW
• P. 458 CE #15
Homework
pg. 458 CE #1-15
WE #1-19 odd
We will review on Monday…
-11.4 Regular polygons, apothems, etc.
-11.5 Circle Area and Circumference
-11.6 Sector area and arclength
-11.7 Ratio of Areas
For a Tuesday Quiz on this Material.
Note: Sculpture Flyer/Alg. 2 Placement Scores