GeometryName______
Notes: Section 11.3 Perimeters & Areas of Similar Figures
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 Find the ratio of the areas.______
Ex 2) These figures are similar. The area of the smaller one is 20. Find the area of the larger picture.
Your turn…
...These 2 figures are similar. The area of the larger figure is 320. Find the area of the smaller figure.
Try it again…
…These 2 figures are similar. The area of the larger figure is 720. Find the area of the smaller figure.
Problem…
…If the figures are similar, what is the length of the side labeled x?
Here’s nothing surprising…
If 2 polygons are similar, the ratio of the perimeters is equal to the ratio of sides.
Perimeter=______Perimeter=______
Ex) ABCD ~ DEFG AB = ______and DE = ______The perimeter of ABCD is 20. What is the
perimeter of DEFG?______
Practice Time:
- 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? ______
- Two figures are similar, ABCDE and XYZWS. The perimeter of ABCDE is and the perimeter of XYZWS is 18. What is the ratio of the corresponding sides (the scale factor)?______
- JKL ~ RST. The area of JKL is 25 and the area of RST is 64. What is the ratio of the perimeters?______
- 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:
- 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? ______
- Two figures are similar, ABCDE and XYZWS. The perimeter of ABCDE is and the perimeter of XYZWS is 18. What is the ratio of the corresponding sides (the scale factor)?______
- JKL ~ RST. The area of JKL is 25 and the area of RST is 64. What is the ratio of the perimeters?______
- 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? ______
- 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 $______
- 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.
- 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 $______
- 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.