Perimeter and Area_ Tutorial
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School
University of South Carolina *
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Course
MISC
Subject
Mathematics
Date
Apr 3, 2024
Type
Pages
7
Uploaded by DeaconFalcon4141
3/20/24, 11:24 AM
Lesson Activity: Maximizing Area
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Lesson Activity
Maximizing Area
This activity will help you meet this educational goal:
You will maximize the area of a figure in a design problem.
Directions
Read the instructions for this self-checked activity. Submit your response to each question
and check your answers. At the end of the activity, write a brief evaluation of your work.
Activity
Chad wants to build a protected area for his new kitten to play in. He has enough materials
to create a structure with a perimeter of 20 feet. Since the building materials are flexible,
Chad can design the structure in any shape. His goal, though, is to provide the kitten with the
largest possible play area.
Use GeoGebra to explore different shapes that he can build. Open maximizing area to
complete each part of the activity. For help, watch this video on using GeoGebra to draw
figures and measure area .
Question
3/20/24, 11:24 AM
Lesson Activity: Maximizing Area
https://f1.app.edmentum.com/courseware-delivery/ua/135055/45616255/aHR0cHM6Ly9mMS5hcHAuZWRtZW50dW0uY29tL2x0aS92Mi9sZWFybmV…
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Part A
Chad tries designing quadrilateral pens first. Use GeoGebra to draw
quadrilateral
with
each set of coordinates and find the perimeter and area. Then complete the table by typing
the correct answer in each box. Use numerals instead of words.
A
B
C
D
Perimeter
Area
units
units
units
units
units
units
units
units
Correct!
Explanation:
In GeoGebra, use the polygon tool to create each figure. Then use the measurement
tools to find the perimeter and area.
A
B
C
D
Perimeter
Area
20 units
24 units
20 units
20 units
20 units
25 units
20 units
9 units
20
24
2
20
20
2
20
25
2
20
9
2
2
2
2
2
3/20/24, 11:24 AM
Lesson Activity: Maximizing Area
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Part B
Try drawing other quadrilaterals with a perimeter of 20 and calculating their area. Using your
results and the results from part A, what conjecture can you make about the shape that will
maximize the play area? Explain your reasoning.
Answer:
Of all the quadrilaterals, a square with side lengths of 5 feet has the largest area, while maintaining a
perimeter of 20 feet
Space used (includes formatting): 200 / 15000
Of all the quadrilaterals, a square with side lengths of 5 feet has the largest area, while
maintaining a perimeter of 20 feet. Squares are regular polygons. So, to maximize the area of
a polygon-shaped structure, Chad should use a regular polygon in his design.
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Question
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3/20/24, 11:24 AM
Lesson Activity: Maximizing Area
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Part C
Chad decides to try designing with regular polygons to see how the areas compare. Use
GeoGebra to draw the figures and find the areas. Then complete the table by typing the
correct answer in each box. Use numerals instead of words. Round values to the nearest
hundredth.
Regular Figure
Number of
Sides
Side
Length
Perimeter
Area
quadrilateral
4
5
units
units
pentagon
5
<
4
units
units
decagon
10
2
units
units
icosagon
20
1
units
units
Correct!
Explanation:
In GeoGebra, use the regular polygon tool to create each figure. Then use the
measurement tools to find the perimeter and area.
Regular Figure
Number of
Sides
Side
Length
Perimeter
Area
quadrilateral
4
5
20 units
25 units
pentagon
5
4
20 units
27.53 units
decagon
10
2
20 units
30.78 units
icosagon
20
1
20 units
31.57 units
20
25
2
20
27.53
2
20
30.78
2
20
31.57
2
2
2
2
3/20/24, 11:24 AM
Lesson Activity: Maximizing Area
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3/20/24, 11:24 AM
Lesson Activity: Maximizing Area
https://f1.app.edmentum.com/courseware-delivery/ua/135055/45616255/aHR0cHM6Ly9mMS5hcHAuZWRtZW50dW0uY29tL2x0aS92Mi9sZWFybmV…
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Part D
Consider your results from part C and what happens to both the shape and the area
measurement as the number of sides increases. What conjecture can you make about the
shape that will maximize the play area? Explain your reasoning.
Answer:
As the number of sides increases, the area of the regular polygon increases, while still maintaining a
perimeter of 20 feet
Space used (includes formatting): 161 / 15000
As the number of sides increases, the area of the regular polygon increases, while still
maintaining a perimeter of 20 feet. As the number of sides increases, the regular polygon
itself also starts looking more and more like a circle. It appears that to maximize the play
area, Chad should design a circular play area with a circumference of 20 feet.
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Self-Evaluation
How did you do? Rate your work on a scale of 1 to 5, with 5 as the highest score. Then write a
brief evaluation of your work below. Note what you learned and what challenged you.
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3/20/24, 11:24 AM
Lesson Activity: Maximizing Area
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Answer:
5, I worked hard got all answers right and think i did very good
Space used (includes formatting): 77 / 15000