Finding the Area of a Garden

Question

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: (1 point)
a. A (-7, 6)
b. B (-2, -6)
c. C (10, -1)
d. D (5, 11)
2. Connect the points to create Square ABCD. (1 point)

3. SHOW YOUR WORK: Use the Pythagorean Theorem to find the side length, s, of Square ABCD in feet. (3 points)

s = ________feet
4. SHOW YOUR WORK: Use the area formula, A = s2, to find the area of Square ABCD. (1 point)

A = ________feet2

Answer 1

1. The points A (-7, 6), B (-2, -6), C (10, -1), and D (5, 11) are plotted on the grid as shown.

2. Connect the points A, B, C, and D to create Square ABCD.

3. To find the side length of Square ABCD in feet, we can use the distance formula or the Pythagorean Theorem.
Using the distance formula, we have:
AB = √((-2 - (-7))^2 + (-6 - 6)^2) = √(5^2 + 12^2) = √(25 + 144) = √169 = 13 feet

Therefore, the side length of Square ABCD is 13 feet.

4. To find the area of Square ABCD, we can use the area formula A = s^2, where s is the side length of the square.
A = 13^2 = 169 square feet

Therefore, the area of Square ABCD is 169 square feet.

Answer 2

. SHOW YOUR WORK: Use the Pythagorean Theorem to find the side length, s, of Square ABCD in feet.

Answer 3

To find the side length of Square ABCD using the Pythagorean Theorem, we need to find the distance between two of the points on a side of the square.

Let's find the distance between points A (-7, 6) and B (-2, -6):

The horizontal distance between the points is 7 - (-2) = 9 units.
The vertical distance between the points is 6 - (-6) = 12 units.

Using the Pythagorean Theorem, we can find the distance between the points:
Distance = √(horizontal distance^2 + vertical distance^2)
Distance = √(9^2 + 12^2)
Distance = √(81 + 144)
Distance = √(225)
Distance = 15 units.

Therefore, the side length (s) of Square ABCD is 15 units (or feet).