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Geometry
Notes: Section 11.3 Perimeters & Areas of Similar Figures
Name________________________
Goals:
 Compare _____________ and _______________ of ________________ figures.

Use ______________ and _____________ to solve _______________.
Investigation:
 Draw a rectangle that is 3 x 2 …
 Find its area…________
 Draw a rectangle that 6 x 4 …
 Find its area…________
 What lengths of sides were doubled, did the areas doubled?__________
Let’s see what happened…
 Find the ratio of the sides … _________
 Find the ratio of the areas … __________
 Theorem: The Area of similar Polygons:
If 2 polygons are ______________ with lengths of _________________ sides to be in the ratio of
__________, then the ratio of their areas is ______________ .
Ex 1) ABCDE ~ MNOPQ
C
D
B
E
A
4
Find the ratio of the areas.___________________
O
P
N
M
6
Q
Ex 2) These figures are similar. The area of the smaller one is 20. Find the area of the larger picture.
4
10
Your turn…
...These 2 figures are similar. The area of the larger figure is 320. Find the area of the smaller figure.
5
8
Try it again…
…These 2 figures are similar. The area of the larger figure is 720. Find the area of the smaller figure.
12
5
Problem…
…If the figures are similar, what is the length of the side labeled x?
Remember:
A = 36
4
The ratio of the areas is
the square of the ratios of the sides
OR
The ratio of the sides is the square
A = 100
x
root of the ratio of the areas!
Here’s nothing surprising…
If 2 polygons are similar, the ratio of the perimeters is equal to the ratio of sides.
3
6
2
4
Perimeter=______
Perimeter=______
Ex) ABCD ~ DEFG AB = _______ and DE = _______ The perimeter of ABCD is 20. What is the
perimeter of DEFG?_______
SUMMARY:
 The ratio of the ______________ of similar figures is the ____________ of the ratio of the sides.
 The ratio of the ______________ of similar figures is the ________ as the ratio of the sides.
 The ratio of the _____________ in two similar figures is the __________ _______ of the ratio of
the areas.
Practice Time:
1. RATS ~ DOGS, RA = 12 and DO = 30.
a. What is the ratio of the perimeters of RATS to DOGS? ______________
b. What is the ratio of the areas of RATS to DOGS? ______________
2. Two figures are similar, ABCDE and XYZWS. The perimeter of ABCDE is 3 3 and the
perimeter of XYZWS is 18. What is the ratio of the corresponding sides (the scale
factor)?_______________
3. JKL ~ RST. The area of JKL is 25 and the area of RST is 64. What is the ratio of the
perimeters?_________
4. HOT ~ DOG. The area of HOT is 100 and the area of DOG is 9. The perimeter of HOT is 40.
What is the perimeter of DOG? ____________________
Practice Time:
1. RATS ~ DOGS, RA = 12 and DO = 30.
a. What is the ratio of the perimeters of RATS to DOGS? ______________
b. What is the ratio of the areas of RATS to DOGS? ______________
2. Two figures are similar, ABCDE and XYZWS. The perimeter of ABCDE is 3 3 and the
perimeter of XYZWS is 18. What is the ratio of the corresponding sides (the scale
factor)?_______________
3. JKL ~ RST. The area of JKL is 25 and the area of RST is 64. What is the ratio of the
perimeters?_________
4. HOT ~ DOG. The area of HOT is 100 and the area of DOG is 9. The perimeter of HOT is 40.
What is the perimeter of DOG? ____________________
5.
You want to carpet a room that measures 40 ft by 48 ft. An advertisement states tahtt the cost to carpet a room that
measures 10 ft by 12 ft is $126. What is a reasonable cost for the larger room?
Solution: The ratio of the lengths of corresponding sides are ______________.
What is the ratio of the side lengths?__________The ratio of the areas?___________
The carpet for the larger room should cost about ____________ times that of the smaller room.
_____________ x ________________ = _________________
A reasonable cost for the larger room is $_____________
6.
A park has two gazebos. The floor of each gazebo has the shape of a regular hexagon. The floor of one gazebo has a
perimeter of 72 ft and an area of about 374.12 square feet. The floor of the larger gazebo has a perimeter of 96 feet.
Find its area.
Solution: All regular hexagons are __________________ because all corresponding angles are _______________ and
the corresponding side lengths are _____________________.
a) Find the ratio of the perimeters of the two gazebos:_________________
b) Calculate the area of the larger gazebo:
(Let A represent the area of the larger gazebo.)
The ratio of the area of the smaller gazebo to area larger is: _______ : _______ or _______ : _______
Therefore, the area of the larger gazebo is about _________________ square feet.
5.
You want to carpet a room that measures 40 ft by 48 ft. An advertisement states tahtt the cost to carpet a room that
measures 10 ft by 12 ft is $126. What is a reasonable cost for the larger room?
Solution: The ratio of the lengths of corresponding sides are ____________________________.
What is the ratio of the side lengths?____________ The ratio of the areas?_____________
The carpet for the larger room should cost about ____________ times that of the smaller room.
_____________ x ________________ = _________________
A reasonable cost for the larger room is $_____________
6.
A park has two gazebos. The floor of each gazebo has the shape of a regular hexagon. The floor of one gazebo has a
perimeter of 72 ft and an area of about 374.12 square feet. The floor of the larger gazebo has a perimeter of 96 feet.
Find its area.
Solution: All regular hexagons are __________________ because all corresponding angles are _______________ and
the corresponding side lengths are _____________________.
a) Find the ratio of the perimeters of the two gazebos:_________________
b) Calculate the area of the larger gazebo:
(Let A represent the area of the larger gazebo.)
The ratio of the area of the smaller gazebo to area larger is: _______ : _______ or _______ : _______
Therefore, the area of the larger gazebo is about _________________ square feet.