http://www.ck12.org Chapter 10. Perimeter and Area
CK-12 Foundation: Chapter10AreaandPerimeterofSimilarPolygonsB
Concept Problem Revisited
You should end up with an 18in× 18 indrawing of your handprint.
Vocabulary
Perimeteris the distance around a shape. The perimeter of any figure must have a unit of measurement attached to
it. If no specific units are given (feet, inches, centimeters, etc), write “units.”Areais the amount of space inside a
figure. Area is measured in square units. Polygons aresimilarwhen their corresponding angles are equal and their
corresponding sides are in the same proportion. Similar polygons are the same shape but not necessarily the same
size.
Guided Practice
- 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? - Two triangles are similar. The ratio of the areas is^2564. What is the scale factor?
- Using the ratios from #2, find the length of the base of the smaller triangle if the length of the base of the larger
triangle is 24 units.
Answers:
- 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.
- The scale factor is
√
25
64
=^58.
- All you would need to do is multiply the scale factor we found in #2 by 24.
b=5
8
· 24 = 15 unitsInteractive Practice
MEDIA
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Determine the ratio of the areas, given the ratio of the sides of a polygon.