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11.3 Perimeters and Areas
of Similar Figures
Advanced Geometry
Are the Triangles Similar?
Find the scale factor of the similar
polygons.
Find the ratio of the perimeter and the
areas of the polygons.
THEOREM 11.5
AREAS OF SIMILAR POLYGONS
If two polygons are similar with the lengths of
corresponding sides in the ratio of a:b, then
the ratio of their areas is a2:b2.
Find the ratio of the areas of the
triangles.
Find the Ratio of the areas of the
polygons.
Example
The ratio of corresponding sides of two similar
hexagons is 3:2.
1. Find the ratio of their perimeters.
2. Find the ratio of their areas.
Example
You are buying photographic paper to print a
photo in different sizes. An 8 inch by 10 inch
sheet of the paper costs $.42. What is a
reasonable cost for a 16 inch by 20 inch sheet?
Example
A rectangular tablecloth is 60 in. by 120 in. A
rectangular place mat made from the same
cloth is 12 in. by 24 in. and costs $5. Compare
the areas of the place mat and tablecloth to
find a reasonable cost for the tablecloth.
Example
A trading pit at the Chicago Board of Trade is
in the shape of a series of regular octagons.
One octagon has a side length of about 14.25
feet and an area of about 980.4 square feet.
Find the area of a smaller octagon that has a
perimeter of about 76 feet.
Example
A store sells trampolines that are all regular
hexagons. One trampoline has a side length
of about 4.5 ft and an area of about 52.6 ft2.
Find the area of the trampoline whose
perimeter is 67.5 ft.
Example
Two similar polygons have perimeters of 7 cm
and 28 cm respectively. Find the area of the
smaller figure if the area of the larger is 48
cm2.