Question

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.
s = ________feet
4. Use the area formula, 𝐴𝐴= 𝑠𝑠2, to find the area of Square ABCD.
A = ________feet^2

Answer 1

To solve the problem, we need to follow the steps provided.

### 1. Plot and Label the Points
Let's plot the given points on the grid:

- Point A: (-7, 6)
- Point B: (-2, -6)
- Point C: (10, -1)
- Point D: (5, 11)

### 2. Connect the Points to Create Square ABCD
Upon plotting these points on the coordinate grid, you will want to connect them in the order A, B, C, D to create the shape of the square. It’s important to note that the points need to correspond to the correct arrangement of a square.

### 3. Use the Pythagorean Theorem to Find Side Length, s
To find the length of one side of the square, we should calculate the distance between two adjacent points using the distance formula:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

We'll need to identify two points that would give us the side length of the square. For this case, let's use points A and B:

- A: (-7, 6)
- B: (-2, -6)

Now, substituting into the formula:
\[
s = d(A, B) = \sqrt{((-2) - (-7))^2 + ((-6) - 6)^2}
\]
Calculating:
\[
s = \sqrt{(-2 + 7)^2 + (-6 - 6)^2}
\]
\[
s = \sqrt{(5)^2 + (-12)^2}
\]
\[
s = \sqrt{25 + 144}
\]
\[
s = \sqrt{169}
\]
\[
s = 13 \text{ feet}
\]

### 4. Use the Area Formula, A = s^2
Now, using the area formula for a square:
\[
A = s^2 = 13^2 = 169 \text{ feet}^2
\]

### Final Results
Now we can summarize our findings:

- **s = 13 feet**
- **A = 169 feet²**

So the answers to your questions are:
- **s = 13 feet**
- **A = 169 feet²**