The Pythagorean Theorem Portfolio
Use the worksheet to record your answers to the four activities that make up the Pythagorean Theorem Portfolio. When you are finished, save the worksheet with your answers and submit it for a portfolio grade.
Finding the Area of a Field
Farmers need to know the area of their land in order to plan for growing their crops. Farmers measure the size of their fields in acres. One acre is equal to 4,840 square yards. In the diagram on the worksheet, each of the squares in the grid represents one acre. Count the number of acres inside Fields A and B to find their measure, and then use that information to find the size of Field C.
Count the number of squares inside Field A. This is the area of Field A in acres. Write it on your worksheet.
Count the number of squares inside Field B. This is the area of Field B in acres. Write it on your worksheet.
Use the Pythagorean Theorem to find the area of Field C in acres.
Finding the Area of a Garden
You can use the Pythagorean Theorem to find the area of a square when you know its end points.
A square garden has the end points listed below. Plot and label these points on the grid:
A (−7, 6)B (−2, −6)C (10, −1)D (5, 11)
Connect the points to create Square ABCD
.
Use the Pythagorean Theorem to find the side length, s
, of Square ABCD
.
Use the area formula, A = s2
, to find the area of Square ABCD
.
Screen Size
Computer screens and television screens are usually measured by the diagonal of the screen. For example, a screen of size 60 inches would have a diagonal of 60 inches, a width of 52 inches, and a height of 30 inches.
Yoselin would like to install a new screen on a shelf that is 17 inches tall and 50 inches wide. She would like the screen to be the largest size that will fit on the shelf. She knows the diagonal and width of the four screens listed below.
Screen
Diagonal
Width
Height
A
15"
13"
B
22"
19"
C
32"
28"
D
40"
35"
Use the Pythagorean Theorem to calculate the height of each screen.
Which screen is the largest that will fit on Yoselin’s shelf?
Building a Ramp
Emaniee would like to build a ramp for her dog over some stairs.
Compute the distance between points B
and C
and enter it on your worksheet.
Compute the distance between points A
and B
and enter it on your worksheet.
Compute the distance between points D
and B
and enter it on your worksheet.
Use the Pythagorean Theorem to compute the distance between points D
and C
.
How long does Emaniee’s ramp need to be?
To complete the Pythagorean Theorem Portfolio, follow the instructions for each activity:
Finding the Area of a Field:
1. Count the number of squares inside Field A. This is the area of Field A in acres. Write it on your worksheet.
2. Count the number of squares inside Field B. This is the area of Field B in acres. Write it on your worksheet.
3. Use the Pythagorean Theorem to find the area of Field C in acres.
Finding the Area of a Garden:
1. Plot and label the end points A (-7, 6), B (-2, -6), C (10, -1), and D (5, 11) on the grid.
2. Connect the points to create Square ABCD.
3. Use the Pythagorean Theorem to find the side length, s, of Square ABCD.
4. Use the area formula, A = s^2, to find the area of Square ABCD.
Screen Size:
1. Use the Pythagorean Theorem to calculate the height of each screen. For each screen, square the diagonal, square the width, square the height, and add the squared width and height together. Take the square root of the sum to find the height.
2. Determine which screen has the largest height that will fit on Yoselin's shelf.
Building a Ramp:
1. Compute the distance between points B and C and enter it on your worksheet.
2. Compute the distance between points A and B and enter it on your worksheet.
3. Compute the distance between points D and B and enter it on your worksheet.
4. Use the Pythagorean Theorem to compute the distance between points D and C.
5. Use the computed distance to determine the length of Emaniee's ramp.
Unfortunately, as an AI language model, I am unable to access or complete worksheets. However, I can provide you with the steps and formulas needed to solve the problems presented in the Pythagorean Theorem Portfolio.
1. Finding the Area of a Field:
- Count the number of squares inside Field A and write down the number as the area of Field A in acres.
- Count the number of squares inside Field B and write down the number as the area of Field B in acres.
- Use the Pythagorean Theorem: c^2 = a^2 + b^2 to find the length of the diagonal (c) of Field C.
- Once you have the length of the diagonal, divide it by the length of each square to find the number of squares inside Field C. Write down this number as the area of Field C in acres.
2. Finding the Area of a Garden:
- Plot and label the given points (A, B, C, D) on the grid.
- Connect the points to create a square ABCD.
- Use the distance formula: d = sqrt((x2 - x1)^2 + (y2 - y1)^2) to find the distance between two consecutive points (e.g., AB, BC, CD).
- The distance between any two consecutive points represents the length of one side of the square.
- Use the formula A = s^2 (where s is the side length) to find the area of Square ABCD.
3. Screen Size:
- Use the Pythagorean Theorem: c^2 = a^2 + b^2 to find the height of each screen.
- Compare the height of each screen to the height of Yoselin's shelf to determine the largest screen that will fit.
4. Building a Ramp:
- Use the distance formula to calculate the distance between points B and C.
- Use the distance formula to calculate the distance between points A and B.
- Use the distance formula to calculate the distance between points D and B.
- Use the Pythagorean Theorem to compute the distance between points D and C.
- The distance between points D and C represents the length of Emaniee's ramp.
Please use these steps and formulas to complete your worksheet.
To answer the question about finding the area of a field, you will need to count the number of squares inside Field A and Field B. Each square represents one acre. Write down the number of squares in each field on your worksheet. Once you have the measurements for Field A and Field B, you can use the Pythagorean Theorem to find the area of Field C by finding the square root of the sum of the squares of the sides. Write down the area of Field C on your worksheet.
For finding the area of a garden, you will be given the coordinates of the end points of a square garden. Plot and label these points on a grid. Then, connect the points to create Square ABCD. Use the Pythagorean Theorem to find the side length of the square by finding the square root of the sum of the squares of the differences in the x-coordinates and y-coordinates of the points. Once you have the side length, you can use the area formula A = s^2 to find the area of Square ABCD. Write down the side length and area on your worksheet.
To calculate the height of each screen for the screen size question, you will use the Pythagorean Theorem. You are given the diagonal and width of each screen. The height can be found by using the Pythagorean Theorem to solve for the height as the square root of the difference between the square of the diagonal and the square of the width. Calculate the height for each screen and write it down. Then, compare the heights to find the largest screen that will fit on Yoselin's shelf.
For building a ramp, you will need to compute the distance between several points. The distances required are: between points B and C, A and B, D and B. Enter these distances on your worksheet. To find the distance between points D and C, you will use the Pythagorean Theorem to find the square root of the sum of the squares of the differences in the x-coordinates and y-coordinates. Once you have the distance between D and C, you will know how long Emaniee's ramp needs to be.