GeomS2 - M09L08 Study Sheet
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Berry College *
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Mathematics
Date
Feb 20, 2024
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docx
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Uploaded by BarristerBraveryBoar12
Name: Owen Davis
Module: 9
Geometry Study Sheet Lesson: 8 Title: Perimeter and Area of Similar Figures
Objective(s)
Today I will:
7.5: Use properties of similar triangles to solve problems. http://moziru.com/images/blur-clipart-speech-bubble-18.jpg
I will know I’ve got it when I can:
Determine the perimeter of similar figures
Determine the area of similar figures
Warm-Up
#1:
Find the perimeter of a rectangle with a length of 6 feet and a width of 9 feet. 30 feet as you would double 6 to get 12 and 9 to get 18 and that equals 30.
#2:
Find the area of a rectangle with a length of 7 feet and a width of 12 feet. You would do 12x7 and get 84ft squared. Vocabulary
Term
Definition
Example
perimeter
perimeter is the length, or distance, around the outside of a two-dimensional figure
area
how much space there is inside a two-dimensional
figure. “You Try” Examples from the Lesson
Ex 1:
A regular octagon has side lengths equal to 5 feet. The perimeter of this octagon is 40 feet. A second regular octagon has side lengths equal to 12.5 feet. What is the perimeter
of the second octagon? Essential Question:
How is similarity of geometric figures applied and verified?
Ex 2: A regular octagon has side lengths equal to 5 feet. The area of this octagon is 120.7 square feet. A second regular octagon has side lengths equal to 12.5 feet. What is the area
of the second octagon?
Independent Practice Problems
For #1 - 5, two similar figures are being compared. Find the requested ratio being described. Justify each of your answers.
1. If the side ratio is 4:17, then the area ratio is 16:298
. It would be 4 squared: 17 squared as we know that you square to find the area, so that means that the answer is 16:298
2. If the side ratio is 9:16, the perimeter ratio is 9:16
. I know this because the ratio of the sides is also the ratio of the perimeter. 3. If the area ratio is 256:361, then the perimeter ratio is 16:19
.
This is the perimeter because I know you need to square to find the area so you will just take the square root of each number to get 16:19. 4. Two similar figures have a side ratio of 3:4. The area of the larger figure is 100 square units. What is the area of the smaller figure?
5. Two similar figures have a side ratio of 4:3. If the perimeter of the smaller figure is 15 units, what is perimeter of the larger figure?
6. Triangle PQR is similar to triangle DEF as shown. Describe the relationship between the corresponding sides of the two triangles.
The following triangles have a ratio of 2:3 as they are similar. 7. Δ PQR
is similar to Δ XYZ
. What is the perimeter of Δ XYZ
?
I can tell that PQ and XY have a scale factor of 6, so I know I need to multiply 10x6 and 6x6 and that gives me with XZ=60 and YZ=36, that means that 30+60+36= 126 for the perimeter of XYZ. 8. Tory has two similar picture frames in her bathroom. The ratio of the larger picture frame to the smaller picture frame is 5:2. If the perimeter of the smaller picture frame is 30 inches, what is the perimeter of the bigger picture frame?
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9. As the marketing designer for Burger King, you are given a 4 inch by 6 inch logo and have been told to create an advertisement with sides six times larger. What is the area of your advertisement (in feet)? [12 inches = 1 ft]
10. Using what you know about the perimeter and area of similar figures, make a conjecture about the volumes of similar figures.
I would assume that you would take the area of the figure and multiply it by the perimeter to get the volume. Summary
I will know I’ve got it when I can:
Rate yourself, using a scale of 1(not at all) to 10 (I
could teach this), on how well you understand each
objective. Note: If you score yourself as a 6 or less for any objective, you should not move on to the next lesson until you have reviewed this lesson and/or, asked questions of the teacher. In addition, if you are not already, you should be regularly attending the weekly Live Sessions or watching the Recordings of past sessions to assist with your understanding of the course concepts. Think back to the lesson itself. What parts of the lesson helped you learn the objectives best?
What questions do you still have? Is there additional information you need to feel more confident with the objectives?