1. SECTION 11-7
RATIOS OF AREAS

2. Theorem 11-7:
If the scale factor of two similar figures is a:b, then
The ratio of the perimeters is a:b
The ratio of the areas is a²:b²
Side Note:
All circles are similar, unless they have the same radius, in which case they’d be congruent!

3. Example 1: The ratio of the perimeters of two similar triangles is 3:5
Example 1: The ratio of the perimeters of two similar triangles is 3:5. Find the scale factor and the ratio of the areas.
Scale Factor = 3:5
Ratio of Areas = 9:25
Example 2: The ratio of the areas of two similar rectangles is 25:36. Find the scale factor and the ratio of the perimeters.
Scale Factor = 5:6
Ratio of Perimeters = 5:6

4. Example 3: RST and XYZ are similar triangles with RS = 8 and XY = 12
Example 3: RST and XYZ are similar triangles with RS = 8 and XY = 12. Find the ratio of their perimeters and areas.
Ratio of Perimeters = 2:3
Scale Factor = 2:3
Ratio of Areas = 4:9
Example 4: Two circles have diameters 6 and 10. Find the ratio of their circumferences.
Ratio of Circumferences = 3:5

5. Example 5: Two circles have radii 5 and 7. Find the ratio of the areas.
Ratio of Areas = 25:49
Example 6: The areas of two circles are 144 and 64. Find the ratio of their circumferences.
Ratio of Radii (or Diameter) = 3:2
Ratio of Circumferences = 3:2

6. Example 7: Find the scale factor and the ratio of the areas.
= 1:3
Ratio of Areas = 1:9 A D B C E 3 6 15 4 9

7. Example 8: Find the scale factor and the ratio of the areas.
Similar b/c of AA ~ Theorem
Scale Factor = 7:12
Ratio of Areas = 49:144 24 14