Name ______________________________________ Date _________________________ Period __________
Section 11-3
Perimeters and Areas of Similar Figures
Recall:

Two polygons are similar iff ____________________________________________________________
____________________________________________________________________________________

The ratio of the lengths of two corresponding sides of two similar polygons is called the
___________________________

The ratio of the _____________________ of two similar polygons is ____________________ as the
___________________________
Areas of Similar Polygons Theorem: ____________________________________________________________
____________________________________________________________
____________________________________________________________
For example: Pentagon ABCDE ~ Pentagon LMNPQ
Scale Factor = ___________
Ratio of the Perimeters = ____________
Ratio of their Areas = ____________
The polygons shown are similar. Find the ratio (shaded to unshaded) of their perimeters and their areas.
1.
2.
Ratio of the Perimeters = ____________
Ratio of the Perimeters = ____________
Ratio of their Areas = ____________
Ratio of their Areas = ____________
3.
4.
Ratio of the Perimeters = ____________
Ratio of the Perimeters = ____________
Ratio of their Areas = ____________
Ratio of their Areas = ____________
Geometry
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If you are given the ratio of the areas, ___________________________________________________________
____________________________________________________________
Solve.
5. The ratio of the lengths of corresponding sides of two similar polygons is 3 : 7 . What is the ratio of their
areas?
6. The ratio of the areas of two similar triangles is 32 : 8 . What is the ratio of the lengths of corresponding
sides?
7. The ratio of the areas of two similar octagons is 64 : 25 . What is the ratio of the lengths of the
corresponding sides?
8. A regular hexagon has an area of 36 square centimeters. Find the scale factor of this hexagon to a similar
hexagon that has an area of 16 square centimeters.
9. The ratio of the lengths of corresponding sides of two similar rectangles is 3 : 5 . The smaller rectangle has
an area of 36 square centimeters. What is the area of the larger rectangle?
10. The ratio of the lengths of corresponding sides of two similar triangles is 5 : 12 . The smaller triangle has
an area of 24 square centimeters. What is the area of the larger triangle?
Complete each statement using always, sometimes, or never.
11. Two similar quadrilaterals _____________________ have the same perimeter.
12. Two squares with the same perimeter are _____________________ similar.
13. Two regular hexagons are _____________________ similar.
14. Two right triangles with the same area are _____________________ similar.
15. Two similar pentagons _____________________ have the same perimeter.
16. Two rectangles with the same area are _____________________ similar.
17. Two regular decagons are _____________________ similar.
18. Two regular polygons are _____________________ similar.
Geometry
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