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 A = ½(20)(12) = 120 12 12 10 20 10 1 60 1 Ratio of bases: = Ratio of areas: = 120 2 20 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 A = ½(20)(10) = 100 15 10 20 20 15 3 150 3 Ratio of heights: = Ratio of areas: = 10 2 100 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 A = ½(6)(8) = 24 10 8 20 16 6 12 2 Scale Factor: 48 2 96 4 2 = = Ratio of areas: = = = Ratio of Perimeters 24 1 24 1 1

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 = 3:12 = 1:4 = 7:2 1. ∆ABC to ∆ABD 2. ∆SEO to ∆GEO 9 same height S E O 5 2 G same base = 3:12 = 1:4 = 7:2 1. ∆ABC to ∆ABD 2. ∆SEO to ∆GEO same height G same base E G S R 7 6 O E S 5 6 4. ∆GES to ∆RES 3. ∆GEO to ∆SEO = 7:6 = 5:6

Exercises (6:9) (3√2)x: (2√7)y 5:9 3x:2z 4x:7y 2:3 (6:9) (3√2)x: 1. 2. 3. 4. 5. 6. 7. 3 : 4 5x : 2y 5 : 9 3x:2z 36 : 81 16x2:49y2 18x2:28y2 (6:9) (3√2)x: (2√7)y 5:9 3x:2z Scale Factor 4x:7y 2:3 (6:9) (3√2)x: (2√7)y Ratio of Perims 5x:2y 4x:7y 3:4 2:3 25x²:4y² 9:16 25:81 Ratio of Areas 9x²:4z²

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 What is the ratio of their areas? Scale Factor: r = 7 r = 8 All circles are similar. Ratio of diameters and circumference is the ratio of their radii. Ratio of areas: 7:8

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