geometry 11.7 ratio of areas. comparing areas of triangles 1020 12 if two triangles have equal...

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