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The image contains questions for a math activity packet involving geometry, area, and perimeter concepts, particularly focusing on using a Geoboard and analyzing different shapes.

Here is a breakdown of the questions in text form:

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### **Activity 1 (Area on a Geoboard) Questions:**

1. **Geoboard Rectangles**:
   Using a 25-peg Geoboard, how many different size rectangles (that are not squares) can you make? Show them and give their areas.  
   - (Hint: Begin by making rectangles with sides parallel to the edges of the Geoboard, then try rectangles that are "tilted," though note that tilted rectangles must have all right angles.)
   
2. **Strategies for Irregular Figures**:
   Describe the strategies you used to find the areas of irregular figures. Did you develop your "toolbox" with new strategies? Did group discussions help? Did you use the same strategy for all figures, or did different shapes require different approaches? Explain.

3. **Choosing a Figure**:
   Pick one of the irregular figures (labeled K or L), calculate its area, and describe how you did it. Include a screenshot if possible.

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### **Activity 2 (Relationships Between Perimeter and Area) Questions:**

4. **Estimating Area and Perimeter**:
   Describe your method for estimating the area and perimeter of the second irregular figure on page 6 of the activity. Include sketches if needed to explain your strategy.

5. **The Banquet Problem**:  
   A family has 18 people for a gathering and rents tables, each seating 4 people. They decide to arrange the tables in a rectangular shape, and they will need 8 tables total (since 8 people can sit on each side and one on each end).  
   - Draw possible table arrangements.
   - **a)** What are the different arrangements for connecting the tables? Draw them and note how many tables would be needed in each case.
   - **b)** If each table costs $10 to rent, which arrangement would be the least expensive?

6. **Area and Perimeter Relationships**:
   - **a)** Can two figures have the same area but different perimeters? If so, provide examples.
   - **b)** Can two figures have the same perimeter but different areas? Provide examples or explain why not.

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Let me know if you'd like help answering any of these questions in detail!

### 5 Follow-up Questions:
1. What is the smallest rectangle you can create on a 25-peg Geoboard, and what is its area?
2. Can you list all the possible rectangle areas (excluding squares) on a Geoboard?
3. How would you handle a tilted rectangle to ensure the right angles are preserved?
4. How do the perimeter and area of irregular shapes compare to regular shapes in complexity?
5. For the banquet problem, what is the most efficient table arrangement to minimize table use?

### Tip:
Remember that perimeter and area are independent properties—changing one doesn't always mean the other changes similarly.

Activity 1 (Area on a Geoboard) and Activity 2 (Relationships Between Perimeter and Area). The questions involve finding different-sized rectangles on a 25-peg Geoboard, describing strategies for irregular figures, and solving a table arrangement problem for a banquet.

This activity involves calculating the area and perimeter of different rectangles using a Geoboard. Explore strategies for irregular figures, solve a banquet problem using table arrangements, and understand the relationship between area and perimeter. Suitable for Grades 5-8 students.

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