Geometry 1-8 Complete Lesson: Perimeter, Circumference, and Area

Solve It!
You and your friend have two choices for wall decorations. You say the decoration on the top will use more wall space. Your friend says the two decorations will use the same amount of wall space.
Who is correct? Explain.

Take Note: Match each formula with the measurement it is used to find.

You may need to zoom out to see all of the items. You can also match each item from the left column by selecting it (clicking it) then selecting (clicking on) its match on the right.

P=2b+2h, or 2(b+h)		perimeter of a square
C=\pi d, or C=2\pi r		aread of a triangle
A=\frac{1}{2}bh		perimeter of a rectangle
P=a+b+c		area of a circle
A=\pi r^2		circumference of a circle
A=bh		area of a square
A=s^2		perimeter of a triangle
P=4s		area of a rectangle

Problem 1 Got It?

Take Note: How do you name a circle? Also, describe what the circle symbol looks like.

Take Note: Which of the following are accurate statements about pi? Select all that apply.

Problem 2 Got It?

Take Note: Summarize the process of finding the perimeter of a polygon in the coordinate plane by using the coordinates of its vertices. You may use the canvas to help illustrate your description.

Problem 3 Got It?
Graph quadrilateral JKLM with vertices
Be sure to include relevant graph detail: label axes and indicate units on both axes.

Problem 3 Got It?

What is the perimeter of quadrilateral JKLM, from the previous item? Enter only a number.

GeoGebra: The vertices of quadrilateral JKLM, from the previous items, are plotted for you on the GeoGebra Math Calculator embedded above. Complete the following steps to verify your solutions from above.

Use the Polygon tool to connect the vertices and construct the quadrilateral.
Note that each segment's length is displayed when the final side of the polygon is created.
Note also that some measurement of the quadrilateral itself is also calculated automatically, but 22 is not the perimeter. It is the area.
To find the area, click on the measurement button (look for the image of a line with cm) and select Distance or Length.
Click on the quadrilateral to calculate the perimeter of the polygon and display it on a label. Note that it is also added to the left sidebar.

What is the perimeter of quadrilateral JKLM?
Enter only a number.

Side Note: The following are insights I gained after visiting with an engineer about the importance of mathematics in his profession.

While calculators and computer applications are used for most modern technical computations, the ability of a human being to quickly analyze the "reasonable-ness" of the results is crucial. Understanding the foundational concepts and formulas behind the computer algorithms ensures that mistakes can be identified quickly to reduce costly and dangerous errors.

Problem 4 Got It?
You are designing a poster that will be 3 yd wide and 8 ft high.
How many square feet of paper do you need to make this poster?

Take Note: Summarize the process of finding the Area of a circle from its diameter.

Problem 5 Got It?
The diameter of a circle is 14 ft.
What is the area of the circle in terms of π?

Problem 5 Got It?
The diameter of a circle is 14 ft.
What is the area of the circle using 3.14 as an approximation of π?
Enter only a number.

Problem 5 Got It?
Reasoning: What is a commonly-used rational approximation of π?
You may use Google.

Take Note: Summarize the Angle Addition Postulate and describe how it can be used when finding the area of irregular shapes.

Problem 6 Got It? What is another way to separate the figure in Problem 6? Mark the figure on the canvas to demonstrate your alternate technique. Label all pertinent information.

Problem 6 Got It? What is the area of the figure?
1. Show how you separate the figure on the canvas.
2. Write the area of the figure in the response field. Enter only a number to represent the area in square feet.

Writing: Describe a real-world situation in which you would need to find a perimeter. On the canvas, create a sketch or upload an image to illustrate your situation.

Writing: Describe a situation in which you would need to find an area. On the canvas, create a sketch or upload an image to illustrate your situation.

Error Analysis: A classmate finds the area of a circle with radius 30 in. to be 900 in.². What error did your classmate make?

Review Lesson 1-7: Find AB to the nearest tenth.

Review Lesson 1-7: Find the coordinates of the midpoint of \overline{AB}.
Write your answer in the following format, with no spaces: (3,2).

Review Lesson 1-6: \overleftrightarrow{BG} is the perpendicular bisector of \overline{WR} at point K.
What is m\angle BKR? Enter only a number.

Review Lesson 1-6: \overleftrightarrow{BG} is the perpendicular bisector of \overline{WR} at point K.
Select two congruent segments.

Vocabulary Review: Identify the shapes that are NOT polygons.

Use Your Vocabulary: Match each sequence of letters on the left with the next consecutive letter on the right.

A, C, E, G,...		P
L, M, N, O,...		R
V, U, T, S,...		I

Use Your Vocabulary:
Area is represented in terms of __________.

Use Your Vocabulary:
Circumference is represented in terms of __________.

Reflection: Math Success

Solve It! You and your friend have two choices for wall decorations. You say the decoration on the top will use more wall space. Your friend says the two decorations will use the same amount of wall space.Who is correct? Explain.

Take Note: Match each formula with the measurement it is used to find. You may need to zoom out to see all of the items. You can also match each item from the left column by selecting it (clicking it) then selecting (clicking on) its match on the right.

Problem 1 Got It?

Problem 1 Got It?

Take Note: How do you name a circle? Also, describe what the circle symbol looks like.

Take Note: Which of the following are accurate statements about pi? Select all that apply.

Problem 2 Got It?

Problem 2 Got It?

Take Note: Summarize the process of finding the perimeter of a polygon in the coordinate plane by using the coordinates of its vertices. You may use the canvas to help illustrate your description.

Problem 3 Got It?Graph quadrilateral JKLM with verticesBe sure to include relevant graph detail: label axes and indicate units on both axes.

Problem 3 Got It?What is the perimeter of quadrilateral JKLM, from the previous item? Enter only a number.

What is the perimeter of quadrilateral JKLM?Enter only a number.

Problem 4 Got It?You are designing a poster that will be 3 yd wide and 8 ft high. How many square feet of paper do you need to make this poster?

Take Note: Summarize the process of finding the Area of a circle from its diameter.

Problem 5 Got It?The diameter of a circle is 14 ft.What is the area of the circle in terms of π?

Problem 5 Got It?The diameter of a circle is 14 ft.What is the area of the circle using 3.14 as an approximation of π?Enter only a number.

Problem 5 Got It?Reasoning: What is a commonly-used rational approximation of π?You may use Google.

Take Note: Summarize the Angle Addition Postulate and describe how it can be used when finding the area of irregular shapes.

Problem 6 Got It? What is another way to separate the figure in Problem 6? Mark the figure on the canvas to demonstrate your alternate technique. Label all pertinent information.

Problem 6 Got It? What is the area of the figure? 1. Show how you separate the figure on the canvas. 2. Write the area of the figure in the response field. Enter only a number to represent the area in square feet.

Writing: Describe a real-world situation in which you would need to find a perimeter. On the canvas, create a sketch or upload an image to illustrate your situation.

Writing: Describe a situation in which you would need to find an area. On the canvas, create a sketch or upload an image to illustrate your situation.

Error Analysis: A classmate finds the area of a circle with radius 30 in. to be 900 in.². What error did your classmate make?

Review Lesson 1-7: Find AB to the nearest tenth.

Review Lesson 1-7: Find the coordinates of the midpoint of \overline{AB}. Write your answer in the following format, with no spaces: (3,2).

Review Lesson 1-6: \overleftrightarrow{BG} is the perpendicular bisector of \overline{WR} at point K.What is m\angle BKR? Enter only a number.

Review Lesson 1-6: \overleftrightarrow{BG} is the perpendicular bisector of \overline{WR} at point K.Select two congruent segments.

Vocabulary Review: Identify the shapes that are NOT polygons.

Use Your Vocabulary: Match each sequence of letters on the left with the next consecutive letter on the right.

Use Your Vocabulary: Area is represented in terms of __________.

Use Your Vocabulary:Circumference is represented in terms of __________.

Reflection: Math Success

Solve It!
You and your friend have two choices for wall decorations. You say the decoration on the top will use more wall space. Your friend says the two decorations will use the same amount of wall space.
Who is correct? Explain.

Take Note: Match each formula with the measurement it is used to find.

You may need to zoom out to see all of the items. You can also match each item from the left column by selecting it (clicking it) then selecting (clicking on) its match on the right.

Problem 3 Got It?
Graph quadrilateral JKLM with vertices
Be sure to include relevant graph detail: label axes and indicate units on both axes.

Problem 3 Got It?

What is the perimeter of quadrilateral JKLM, from the previous item? Enter only a number.

What is the perimeter of quadrilateral JKLM?
Enter only a number.

Problem 4 Got It?
You are designing a poster that will be 3 yd wide and 8 ft high.
How many square feet of paper do you need to make this poster?

Problem 5 Got It?
The diameter of a circle is 14 ft.
What is the area of the circle in terms of π?

Problem 5 Got It?
The diameter of a circle is 14 ft.
What is the area of the circle using 3.14 as an approximation of π?
Enter only a number.

Problem 5 Got It?
Reasoning: What is a commonly-used rational approximation of π?
You may use Google.

Problem 6 Got It? What is the area of the figure?
1. Show how you separate the figure on the canvas.
2. Write the area of the figure in the response field. Enter only a number to represent the area in square feet.

Review Lesson 1-7: Find the coordinates of the midpoint of \overline{AB}.
Write your answer in the following format, with no spaces: (3,2).

Review Lesson 1-6: \overleftrightarrow{BG} is the perpendicular bisector of \overline{WR} at point K.
What is m\angle BKR? Enter only a number.

Review Lesson 1-6: \overleftrightarrow{BG} is the perpendicular bisector of \overline{WR} at point K.
Select two congruent segments.

Use Your Vocabulary:
Area is represented in terms of __________.

Use Your Vocabulary:
Circumference is represented in terms of __________.