http://www.ck12.org Chapter 10. Perimeter and Area
Example 3:Two trapezoids are similar. If the scale factor is^34 and the area of the smaller trapezoid is 81cm^2 , what
is the area of the larger trapezoid?
Solution:First, the ratio of the areas would be
( 3
4) 2
= 169. Now, we need the area of the larger trapezoid. To find
this, we would multiply the area of the smaller trapezoid by the scale factor. However, we would need to flip the
scale factor over to be^169 because we want the larger area. This means we need to multiply by a scale factor that is
larger than one.A=^169 · 81 = 144 cm^2.
Example 4:Two triangles are similar. The ratio of the areas is^2564. What is the scale factor?
Solution:The scale factor is
√
25
64
=^58.
Example 5:Using the ratios from Example 3, find the length of the base of the smaller triangle if the length of the
base of the larger triangle is 24 units.
Solution:All you would need to do is multiply the scale factor we found in Example 3 by 24.
b=5
8
· 24 = 15 unitsKnow What? RevisitedYou should end up with an 18in× 18 indrawing of your handprint.
Review Questions
Determine the ratio of the areas, given the ratio of the sides of a polygon.
1.^35
2.^14
3.^72
4. 116
Determine the ratio of the sides of a polygon, given the ratio of the areas.
- 361
- 814
7.^499 - 14425
This is an equilateral triangle made up of 4 congruent equilateral triangles.
- What is the ratio of the areas of the large triangle to one of the small triangles?