Use the Pythagorean Theorem to find the area of Field C in acres:
Field C = (0, 4) (4, 7) (7, 3) (3, 0)
To calculate the height of each screen using the Pythagorean Theorem, we can use the formula a^2 + b^2 = c^2, where c represents the diagonal of the screen and a and b represent the height and width, respectively.
Screen A:
a^2 + b^2 = c^2
a^2 + 13^2 = 15^2
a^2 + 169 = 225
a^2 = 225 - 169
a^2 = 56
a ≈ √56
a ≈ 7.48 inches
Screen B:
a^2 + b^2 = c^2
a^2 + 19^2 = 22^2
a^2 + 361 = 484
a^2 = 484 - 361
a^2 = 123
a ≈ √123
a ≈ 11.09 inches
Screen C:
a^2 + b^2 = c^2
a^2 + 28^2 = 32^2
a^2 + 784 = 1024
a^2 = 1024 - 784
a^2 = 240
a ≈ √240
a ≈ 15.49 inches
Screen D:
a^2 + b^2 = c^2
a^2 + 35^2 = 40^2
a^2 + 1225 = 1600
a^2 = 1600 - 1225
a^2 = 375
a ≈ √375
a ≈ 19.36 inches
Completing the table:
Screen | Diagonal | Width | Height
A | 15" | 13" | 7.48"
B | 22" | 19" | 11.09"
C | 32" | 28" | 15.49"
D | 40" | 35" | 19.36"
Therefore, the height of each screen is as follows:
- Screen A: 7.48 inches
- Screen B: 11.09 inches
- Screen C: 15.49 inches
- Screen D: 19.36 inches
To find the area of Field C, we can use the Pythagorean Theorem to calculate the lengths of the sides of the field, and then apply the formula for the area of a quadrilateral.
First, let's find the lengths of the sides:
Side AB: To find the length of AB, use the distance formula, which is derived from the Pythagorean Theorem:
AB = √((x2 - x1)^2 + (y2 - y1)^2)
AB = √((4 - 0)^2 + (7 - 4)^2)
AB = √(4^2 + 3^2)
AB = √(16 + 9)
AB = √25
AB = 5
Side BC: Using the same distance formula as above:
BC = √((7 - 4)^2 + (3 - 7)^2)
BC = √(3^2 + (-4)^2)
BC = √(9 + 16)
BC = √25
BC = 5
Side CD: Using the same distance formula as above:
CD = √((3 - 7)^2 + (0 - 3)^2)
CD = √((-4)^2 + (-3)^2)
CD = √(16 + 9)
CD = √25
CD = 5
Side DA: Using the same distance formula as above:
DA = √((0 - 3)^2 + (4 - 0)^2)
DA = √((-3)^2 + 4^2)
DA = √(9 + 16)
DA = √25
DA = 5
Now that we have the lengths of all four sides, we can calculate the area using the formula for the area of a quadrilateral. Since Field C is not a rectangle, we can use the formula for the area of a quadrilateral defined by its vertices:
Area of Field C = 0.5 * [AB * CD + BC * DA]
Area of Field C = 0.5 * [5 * 5 + 5 * 5]
Area of Field C = 0.5 * [25 + 25]
Area of Field C = 0.5 * 50
Area of Field C = 25
Since 1 acre is equal to 43,560 square feet, we can convert the area of Field C from square feet to acres:
Area of Field C in acres = 25 / 43,560
Area of Field C in acres ≈ 0.000573 acres
Therefore, the area of Field C is approximately 0.000573 acres.
Use the Pythagorean Theorem to find the side length, s, of Square ABCD in feet:
A = (-7, 6)
B = (-2, -6)
C = (10, -1)
D = (5, 11)
To find the side length, s, of Square ABCD, we can use the distance formula which is derived from the Pythagorean Theorem.
First, let's find the length of AB:
AB = √((x2 - x1)^2 + (y2 - y1)^2)
AB = √((-2 - (-7))^2 + (-6 - 6)^2)
AB = √(5^2 + (-12)^2)
AB = √(25 + 144)
AB = √169
AB = 13
Since ABCD is a square, all four sides have the same length. Therefore, s = AB = 13 feet.
Therefore, the side length of Square ABCD is 13 feet.
Use the area formula, 𝐴 = 𝑠^2, to find the area of Square ABCD:
A (-7, 6)
B (-2, -6)
C (10, -1)
D (5, 11)
To find the area of Square ABCD, we can use the formula for the area of a square, which is given by 𝐴 = 𝑠^2 where s represents the side length of the square.
From the previous question, we found that the side length of Square ABCD is 13 feet. Therefore, we can substitute this value into the area formula:
𝐴 = 13^2
𝐴 = 169
Therefore, the area of Square ABCD is 169 square feet.
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 4 screens listed below.
Screen Diagonal Width Height
A 15” 13”
B 22” 19”
C 32” 28”
D 40” 35”
1. Use the Pythagorean Theorem to calculate the height of each screen, and
complete the table.
Compute the distance between points B and C and enter it on the worksheet.
To compute the distance between points B and C, we can use the distance formula, which is derived from the Pythagorean Theorem.
Point B: (-2, -6)
Point C: (10, -1)
Distance between B and C = √((x2 - x1)^2 + (y2 - y1)^2)
Distance between B and C = √((10 - (-2))^2 + (-1 - (-6))^2)
Distance between B and C = √((12)^2 + (5)^2)
Distance between B and C = √(144 + 25)
Distance between B and C = √169
Distance between B and C = 13
Therefore, the distance between points B and C is 13.