Directions: Use this worksheet to record answers to the two activities that make up the Pythagorean Theorem Portfolio. When you are finished, save this worksheet with your answers and submit it for a portfolio grade.
Finding the Area of a Field
Use the image to answer to complete the activity.
Count the number of squares inside Field A. This is the area of Square A in acres. Write it below:
Area = acres
Count the number of squares inside Field B. This is the area of Square B in acres. Write it below:
Area = acres
Use the Pythagorean Theorem to find the area of Field C in acres:
Area = a2 + b2 = c2
Area = acres
Use the Pythagorean Theorem to find the area of Field C in acres:
Area = a^2 + b^2 = c^2
Area = acres
Field A= 16
Field B= 9
To find the area of Square A, count the number of squares inside Field A:
Area = 9 acres
To find the area of Square B, count the number of squares inside Field B:
Area = 25 acres
To find the area of Field C using the Pythagorean Theorem:
Let a = length of one side of Square A (which is 3 acres)
Let b = length of one side of Square B (which is 4 acres)
Using the Pythagorean Theorem:
Area = a^2 + b^2 = c^2
Area = 3^2 + 4^2 = 9 + 16 = 25 acres
Therefore, the area of Field C is 25 acres.
To find the area of Field C using the Pythagorean Theorem, we need the lengths of the sides of Field A and Field B.
Given that Field A has an area of 16 acres, we can assume that one side of Field A is 4 acres (since 4^2 = 16).
Similarly, given that Field B has an area of 9 acres, we can assume that one side of Field B is 3 acres (since 3^2 = 9).
Using the Pythagorean Theorem, we can find the length of the hypotenuse of the right triangle formed by Field A and Field B:
c^2 = a^2 + b^2
c^2 = 4^2 + 3^2
c^2 = 16 + 9
c^2 = 25
Therefore, c = 5.
Since Field C is a square, the area of Field C is the square of the length of one side, which is 5.
Area = 5^2 = 25 acres.
Therefore, the area of Field C is 25 acres.
How do you use a grid to you do y to x or x to y
To use a grid to find the y-coordinate given an x-coordinate (x to y), follow these steps:
1. Locate the given x-value on the x-axis of the grid.
2. Draw a vertical line from the x-value to the grid.
3. Identify the y-coordinate where the vertical line intersects the grid.
4. That y-coordinate is the corresponding value for the given x-coordinate.
To use a grid to find the x-coordinate given a y-coordinate (y to x), follow these steps:
1. Locate the given y-value on the y-axis of the grid.
2. Draw a horizontal line from the y-value to the grid.
3. Identify the x-coordinate where the horizontal line intersects the grid.
4. That x-coordinate is the corresponding value for the given y-coordinate.
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 in feet.
Area = a2 + b2 = c2 where c is the side length, s.
s = feet
4. Use the area formula, 𝐴 = 𝑠2, to find the area of Square ABCD.
A = feet
To plot and label the points on the grid:
1. Draw a horizontal line for the x-axis and a vertical line for the y-axis on the grid.
2. Locate point A (-7, 6) by moving 7 units to the left on the x-axis and 6 units upwards on the y-axis. Place a label 'A' at this point.
3. Locate point B (-2, -6) by moving 2 units to the left on the x-axis and 6 units downwards on the y-axis. Place a label 'B' at this point.
4. Locate point C (10, -1) by moving 10 units to the right on the x-axis and 1 unit downwards on the y-axis. Place a label 'C' at this point.
5. Locate point D (5, 11) by moving 5 units to the right on the x-axis and 11 units upwards on the y-axis. Place a label 'D' at this point.
6. Connect the points A, B, C, and D in order to create Square ABCD on the grid.
To find the side length, s, of Square ABCD using the Pythagorean Theorem:
1. Calculate the distance between point A and point B (a side of square):
Distance AB = √[(x2 - x1)^2 + (y2 - y1)^2]
= √[(-2 - (-7))^2 + (-6 - 6)^2]
= √[5^2 + (-12)^2]
= √[25 + 144]
= √169
= 13
2. The side length, s, of Square ABCD is equal to the calculated distance between point A and point B:
s = 13 feet
To find the area of Square ABCD:
The area formula for a square is A = s^2, where s is the side length.
1. Substitute the calculated side length, s = 13, into the area formula:
A = 13^2
= 169
2. The area of Square ABCD is 169 square feet.
Use the Pythagorean Theorem to find the area of Field C in acres:
Area = a2 + b2 = c2
Area = acres
To complete the activity, you need to find the area of Square A, the area of Square B, and the area of Field C using the Pythagorean Theorem.
1. Count the number of squares inside Field A. This will give you the area of Square A in acres. Write down the number of squares you counted.
2. Count the number of squares inside Field B. This will give you the area of Square B in acres. Write down the number of squares you counted.
3. To find the area of Field C, you will use the Pythagorean Theorem. The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b).
4. Identify the sides of Field C that form a right triangle. These sides will be the legs of the triangle, which we can call 'a' and 'b'. Measure the length of sides 'a' and 'b'.
5. Use the Pythagorean Theorem formula, Area = a^2 + b^2 = c^2, to find the area of Field C. Square the values of 'a' and 'b', add them together, and then take the square root of the sum to find the length of side 'c'. Square the length of side 'c' to find the area of Field C in acres.
6. Write the area of Square A, Square B, and Field C in acres on the worksheet.
7. Save the completed worksheet with your answers and submit it for a portfolio grade.