Transcript 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