10.7. Area and Perimeter of Similar Polygons http://www.ck12.org
Example A
The two rectangles below are similar. Find the scale factor and the ratio of the perimeters.
The scale factor is^1624 , which reduces to^23. The perimeter of the smaller rectangle is 52 units. The perimeter of the
larger rectangle is 78 units. The ratio of the perimeters is^5278 =^23.
Example B
Find the area of each rectangle from Example A. Then, find the ratio of the areas.
Asmall= 10 · 16 = 160 units^2
Alarge= 15 · 24 = 360 units^2The ratio of the areas would be^160360 =^49.
The ratio of the sides, or scale factor was^23 and the ratio of the areas is^49.
Example C
Find the ratio of the areas of the rhombi below. The rhombi are similar.
There are two ways to approach this problem. One way would be to use the Pythagorean Theorem to find the length
of the 3rdside in the triangle and then apply the area formulas and make a ratio. The second, and easier way, would
be to find the ratio of the sides and then square that.
( 3
5) 2
= 259
Watch this video for help with the Examples above.
MEDIA
Click image to the left for use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/52491