http://www.ck12.org Chapter 11. Surface Area and Volume
Solution:Match up the corresponding heights, widths, and lengths to see if the rectangular prisms are proportional.
small prism
large prism=
3
4. 5
=
4
6
=
5
7. 5
The congruent ratios tell us the two prisms are similar.
Example 2:Determine if the two triangular pyramids similar.
Solution:Just like Example 1, let’s match up the corresponding parts.
6
8 =
12
16 =3
4 however,8
12 =2
3.
Because one of the base lengths is not in the same proportion as the other two lengths, these right triangle pyramids
are not similar.
Surface Areas of Similar Solids
Recall thatwhen two shapes are similar, the ratio of the area is a square of the scale factor.
For example, the two rectangles to the left are similar because their sides are in a ratio of 5:8. The area of the larger
rectangle is 8( 16 ) = 128 units^2 and the area of the smaller rectangle is 5( 10 ) = 50 units^2. If we compare the areas
in a ratio, it is 50 : 128=25 : 64= 52 = 82.
So, what happens with the surface areas of two similar solids? Let’s look at Example 1 again.
Example 3:Find the surface area of the two similar rectangular prisms.