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)
Area = a2 + b2 = c2 where c is the side length, s.
s = ____ feet
The distance formula can be used to find the length of each side of the square:
AB = √((x2 - x1)^2 + (y2 - y1)^2)
BC = √((x2 - x1)^2 + (y2 - y1)^2)
CD = √((x2 - x1)^2 + (y2 - y1)^2)
DA = √((x2 - x1)^2 + (y2 - y1)^2)
Using the given coordinates, we can calculate the distances:
AB = √((-2 - (-7))^2 + (-6 - 6)^2)
= √(5^2 + (-12)^2)
= √(25 + 144)
= √169
= 13
BC = √(10 - (-2))^2 + (-1 - (-6))^2)
= √(12^2 + 5^2)
= √(144 + 25)
= √169
= 13
CD = √(5 - 10)^2 + (11 - (-1))^2)
= √((-5)^2 + 12^2)
= √(25 + 144)
= √169
= 13
DA = √((-7) - 5)^2 + (6 - 11)^2)
= √((-12)^2 + (-5)^2)
= √(144 + 25)
= √169
= 13
Since all sides of the square have the same length, s = AB = BC = CD = DA = 13 feet.
Use the area formula, 𝐴 = 𝑠2, to find the area of Square ABCD.
To find the area of Square ABCD, we can use the side length that we previously found, which is s = 13 feet.
The area formula for a square is given by A = s^2, where A is the area and s is the side length.
Plugging in s = 13, we get:
A = (13)^2
A = 169 square feet.
Therefore, the area of Square ABCD is 169 square feet.
To find the side length, s, of Square ABCD using the Pythagorean Theorem, we need to calculate the distance between points A and B (a), and between points A and D (b). Then, we can use the formula s = sqrt(a^2 + b^2) to find the side length, where sqrt represents the square root function.
First, let's find the distance between points A and B:
a = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Substituting the coordinates of points A (-7, 6) and B (-2, -6) into the formula:
a = sqrt((-2 - (-7))^2 + (-6 - 6)^2)
a = sqrt(5^2 + (-12)^2)
a = sqrt(25 + 144)
a = sqrt(169)
a = 13
Next, let's find the distance between points A and D:
b = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Substituting the coordinates of points A (-7, 6) and D (5, 11) into the formula:
b = sqrt((5 - (-7))^2 + (11 - 6)^2)
b = sqrt(12^2 + 5^2)
b = sqrt(144 + 25)
b = sqrt(169)
b = 13
Now, we can substitute the values of a and b into the formula s = sqrt(a^2 + b^2):
s = sqrt(13^2 + 13^2)
s = sqrt(169 + 169)
s = sqrt(338)
s ≈ 18.38
Therefore, the side length, s, of Square ABCD is approximately 18.38 feet.