You can use the Pythagorean Theorem to find the area of a square when you know its end points.
1. 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)
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.
To find the side length of Square ABCD using the Pythagorean Theorem, we need to calculate the distance between two of the points on the square.
Let's use points A (-7, 6) and B (-2, -6) to find the side length.
Using the distance formula, the distance between two points (x1, y1) and (x2, y2) is given by:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Here, x1 = -7, y1 = 6, x2 = -2, and y2 = -6.
Applying the formula:
d = √((-2 - (-7))^2 + (-6 - 6)^2)
= √((5)^2 + (-12)^2)
= √(25 + 144)
= √169
= 13
Therefore, the side length of Square ABCD is 13 units.
To find the area of Square ABCD, we can use the formula A = s^2, where s is the side length.
Using s = 13, we have:
A = 13^2
A = 169 square units
The area of Square ABCD is 169 square units.