Question

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

Answer 1

Use the area formula, 𝐴 = 𝑠2, to find the area of Square ABCD.

Answer 2

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.

Answer 3

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.