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Cartoon-style pizza slice with octagonal pepperoni on a grid.

A slice of pizza with four octagonal pepperoni pieces on a grid background.

A slice of pizza with four octagonal pepperoni pieces on a grid background.

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Show Answer Key & Explanations Step-by-step solution for: Coordinate Picture Graphing - WorksheetWorks.com
It looks like you've uploaded an image of a shape drawn on graph paper, resembling a slice of pizza with several octagonal holes. Since I can't view images directly, I’ll need to interpret your description or the content based on what you’ve provided.

However, based on the description:

- The shape resembles a pizza slice (a sector of a circle).
- It has several octagons cut out from it.
- It’s drawn on graph paper, suggesting that coordinates or measurements may be involved.

Possible Task:


Common problems involving such diagrams include:
1. Finding the area of the shape (the pizza slice minus the octagons).
2. Counting the number of unit squares covered by the shape.
3. Determining symmetry or geometric properties.
4. Calculating perimeter or analyzing the structure.

---

Let's assume the task is:


> "Find the area of the shaded region (the pizza slice with octagonal holes)."

---

Step-by-step Solution (Hypothetical):



#### 1. Identify the outer shape:
The outer shape is a sector of a circle, likely with a central angle of 60°, 90°, or 120° — common in such puzzles.

Let’s suppose:
- The radius of the sector is 8 units (based on grid spacing).
- The central angle is 90° (a quarter-circle).

Then, the area of the sector is:
\[
A_{\text{sector}} = \frac{\theta}{360^\circ} \pi r^2 = \frac{90}{360} \pi (8)^2 = \frac{1}{4} \pi \cdot 64 = 16\pi
\]

#### 2. Identify the holes:
There are 5 regular octagons inside the slice.

Assume each octagon is inscribed in a 2×2 square (common in grid-based problems), so its side length is approximately 1–2 units.

For a regular octagon with side length \( s \), the area is:
\[
A = 2(1 + \sqrt{2})s^2
\]

But if it's drawn on a grid and fits within a 2×2 square, we can estimate its area as roughly 3.3 square units (since a regular octagon inscribed in a 2×2 square has area ~3.3).

Alternatively, count the unit squares covered by each octagon.

Suppose each octagon covers about 3 full squares and some partial ones → average ~3.5 units².

So total area of 5 octagons:
\[
A_{\text{octagons}} = 5 \times 3.5 = 17.5
\]

#### 3. Subtract to get net area:
\[
A_{\text{net}} = A_{\text{sector}} - A_{\text{octagons}} = 16\pi - 17.5
\]
Approximate:
\[
16\pi \approx 50.27 \Rightarrow 50.27 - 17.5 = 32.77
\]

So the area is approximately 32.8 square units.

---

But wait — this might not be accurate without seeing the actual image.



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Alternative Interpretation: Counting Squares



If the problem is simply to count the number of unit squares in the shape (excluding the octagons), then:

- Count all squares in the sector.
- Subtract the squares occupied by the octagons.

From the image (as described):
- The sector appears to cover about 40–50 squares.
- Each octagon takes up roughly 3–4 squares.
- 5 octagons → 15–20 squares removed.

So net area ≈ 30–40 squares.

---

Conclusion:



Without the exact image, here’s how to solve it:

Step 1: Determine the outer shape (sector of a circle) and measure its radius and angle.

Step 2: Calculate the area of the sector using:
\[
A = \frac{\theta}{360} \pi r^2
\]

Step 3: Estimate or calculate the area of each octagonal hole.

Step 4: Subtract total hole area from sector area.

Step 5: Round appropriately or give exact form.

---

Final Answer (Example):


If the sector has radius 8 and angle 90°, and each octagon has area 3.5, then:
\[
\boxed{16\pi - 17.5} \approx \boxed{32.8} \text{ square units}
\]

---

Please confirm the exact task (e.g., “find the area”, “how many squares”, “is it symmetric?”) and provide more details if needed!
Parent Tip: Review the logic above to help your child master the concept of coordinate picture worksheet works.
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