https://file.aiquickdraw.com/mathbot/file/1728756295035zshxfxg7.jpg

Let's break down and solve each part of the question based on the image provided.

### 9.1. **Name the quadrilateral formed by these bases.**

The bases form a **square**. Since all sides are equal (27.4 m each), the quadrilateral formed is a square.

---

### 9.2. **How far is the distance from home base to the second base if you move directly between the two bases?**

The distance between the home base and the second base is the diagonal of the square. To find the diagonal \( d \) of a square with side length \( s \), we use the Pythagorean theorem:
\[
d = s\sqrt{2}
\]
Given that \( s = 27.4 \, \text{m} \), the diagonal is:
\[
d = 27.4 \times \sqrt{2} \approx 27.4 \times 1.414 \approx 38.73 \, \text{m}
\]
So, the distance from the home base to the second base is approximately **38.73 meters**.

---

### 9.3. **Find the perimeter around the bases of the baseball field.**

Since the quadrilateral is a square, the perimeter \( P \) is given by:
\[
P = 4 \times \text{side length}
\]
\[
P = 4 \times 27.4 \, \text{m} = 109.6 \, \text{m}
\]
Thus, the perimeter around the bases is **109.6 meters**.

---

### 9.4. **Determine the area covered by the bases.**

The area \( A \) of a square is given by:
\[
A = \text{side length}^2
\]
\[
A = 27.4^2 = 750.76 \, \text{m}^2
\]
So, the area covered by the bases is **750.76 square meters**.

---

Let me know if you'd like further details on any step or if you have any questions!

### Additional Questions:
1. What other quadrilaterals have diagonals that use the Pythagorean theorem for diagonal calculation?
2. How can you calculate the diagonal of a rectangle if its sides are different lengths?
3. In what other sports might similar geometry (square layout) be found?
4. How could you calculate the diagonal of a regular pentagon?
5. How would the calculations change if the bases formed a rectangle instead of a square?

### Tip:
Whenever you're asked to find the diagonal of a square, remember it’s always \( \sqrt{2} \) times the side length. This trick saves you time!

A school plans to introduce baseball as one of the sporting codes. The proposed plan shows the layout of a baseball field with the bases forming a square. The problem asks for the name of the quadrilateral formed, the diagonal distance between the bases, the perimeter, and the area covered by the bases.

Explore the geometry of a baseball field by calculating the perimeter, area, and diagonal of a square formed by the bases. Learn how to apply the Pythagorean Theorem and geometric formulas in this practical sports-related problem. Suitable for students in Grades 7-10.

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