Finding the Area of a Garden
Use the image to complete the activity.
1. A square garden has the end points listed below. Plot and label these points on
the grid:
a. A (-7, 6)
b. B (-2, -6)
c. C (10, -1)
d. 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 in
feet.
To find the side length of Square ABCD, we can use the distance formula, which is derived from the Pythagorean theorem.
The distance formula is √[(x2 - x1)^2 + (y2 - y1)^2].
For side AB:
x1 = -7, y1 = 6 (point A)
x2 = -2, y2 = -6 (point B)
Using the distance formula, we have AB = √[(-2 - (-7))^2 + (-6 - 6)^2]
= √[5^2 + (-12)^2]
= √[25 + 144]
= √169
= 13 feet
For side BC:
x1 = -2, y1 = -6 (point B)
x2 = 10, y2 = -1 (point C)
Using the distance formula, we have BC = √[(10 - (-2))^2 + (-1 - (-6))^2]
= √[12^2 + 5^2]
= √[144 + 25]
= √169
= 13 feet
For side CD:
x1 = 10, y1 = -1 (point C)
x2 = 5, y2 = 11 (point D)
Using the distance formula, we have CD = √[(5 - 10)^2 + (11 - (-1))^2]
= √[(-5)^2 + 12^2]
= √[25 + 144]
= √169
= 13 feet
For side DA:
x1 = 5, y1 = 11 (point D)
x2 = -7, y2 = 6 (point A)
Using the distance formula, we have DA = √[(-7 - 5)^2 + (6 - 11)^2]
= √[(-12)^2 + (-5)^2]
= √[144 + 25]
= √169
= 13 feet
Since all sides of Square ABCD have the same length of 13 feet, the side length, s, of Square ABCD is 13 feet.