geometry 11.7 ratio of areas. comparing areas of triangles 1020 12 if two triangles have equal...
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Geometry
11.7Ratio of Areas
Comparing Areas of Triangles
10 20
12 12
If two triangles have equal heights, then the ratio of their areas equals the ratio of their bases.
A = ½(10)(12) = 60 A = ½(20)(12) = 120
Ratio of bases: 20
10 =2
1Ratio of areas:
12060 =
21
Comparing Areas of Triangles
20 20
1510
If two triangles have equal bases, then the ratio of their areas equals the ratio of their heights.
A = ½(20)(15) = 150 A = ½(20)(10) = 100
Ratio of heights: 15
10=
3
2Ratio of areas: 150
100=
3
2
Comparing Areas of Triangles
12
6
168
If two triangles are similar, then the ratio of their areas equals the square of their scale factor.
A = ½(12)(16) = 96A = ½(6)(8) = 24
Scale Factor: 2
1Ratio of areas: 96
24=
4
1=
2
1
2
2010
P = 12 + 16 + 20 = 48P = 6 + 8 + 10 = 24
= Ratio of Perimeters
48
24==
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
1. ∆ABC to ∆ABD
2. ∆SEO to ∆GEO
3. ∆GEO to ∆SEO
4. ∆GES to ∆RES
= 1:4
A
B C D3 9
S
E O
5
2
G
same heightsame base
E
G S S
R7
6
5 6
same heightsame baseG
E
= 7:2
= 5:6= 7:6
= 3:12
O
Exercises
1. 2. 3. 4. 5. 6. 7.
3 : 4 5x : 2y
5 : 9 3x:2z
36 : 81 16x2:49y2 18x2:28y2
Scale Factora
b
Ratio of Perims a
b
Ratio of Areas
2a
b
3:4
9:16
5:9
25:81
(6:9) 2:3
(6:9) 2:3
5x:2y
25x²:4y²
3x:2z
9x²:4z²
4x:7y
4x:7y(3√2)x:(2√7)y
(3√2)x:(2√7)y
Exercises
All circles are similar.
Two circles have areas 49π and 64π. What is the ratio of the diameters and of the circumferences?
The lengths of two similar hexagons are
8.
r = 7r = 8
Ratio of diameters and circumference is the ratio of their radii. 7:8
9.
2 4 4x : x yWhat is the ratio of their areas?
Scale Factor: 2
4 4 2 4
x 1=
x y x y
Ratio of areas:
2 4 4 8
21 1
x y 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