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Let's go through the three questions on your worksheet and solve them one by one.

### 1. Question 1:
**Problem:**  
Joseph uses a scale of 2 cm for every 5 in. What is the actual area of the space for Joseph’s new grill in square inches?

**Solution:**  
We are given the dimensions of the drawing:  
- Length of the grill: 10 cm
- Width of the grill: 18 cm

The scale is 2 cm = 5 in. To convert the drawing dimensions to actual dimensions, we use the scale:
1. Actual length = \( \frac{10 \text{ cm} \times 5 \text{ in}}{2 \text{ cm}} = 25 \text{ in} \)
2. Actual width = \( \frac{18 \text{ cm} \times 5 \text{ in}}{2 \text{ cm}} = 45 \text{ in} \)

Now, the area of the actual grill space is:
\[
\text{Area} = 25 \text{ in} \times 45 \text{ in} = 1125 \text{ in}^2
\]

So, the actual area for Joseph’s grill space is **1125 square inches**.

---

### 2. Question 2:
**Problem:**  
The scale is 8 m for every 2 in. The actual area of the exercise mat is 144 m². What are the dimensions of the mat on the scale copy?

**Solution:**  
We know the actual area is 144 m², and the scale is 8 meters for every 2 inches. 

The actual mat area in real life can be expressed as:
\[
\text{Area} = \text{Length} \times \text{Width} = 144 \text{ m}^2
\]
The scaled length is calculated by converting from meters to inches using the scale \( \frac{8 \text{ m}}{2 \text{ in}} \), or 4 m/in.

If the actual length of one side is \( l \) meters and the other side is \( w \) meters, we find that:
\[
l \times w = 144 \text{ m}^2
\]
We can then convert the side lengths into inches using the scale and determine the scaled dimensions.

---

### 3. Question 3:
**Problem:**  
The Hamiltons are paving a rectangular and parallelogram-shaped area for their driveway. The scale of the sketch is 1 in. = 3 ft. What is the actual area of the driveway?

**Solution:**  
In this question, we need the dimensions of the rectangular and parallelogram-shaped areas from the diagram. Then, we can use the scale 1 in = 3 ft to find the actual dimensions and compute the areas of both the rectangle and the parallelogram, and then sum them to get the total area.

Would you like more details or assistance with a specific part of these problems?

Here are 5 related questions to expand your understanding:
1. How would you convert between different units when working with scales?
2. What is the significance of using scale drawings in real-life applications?
3. How does the area scale change with the change in the linear dimensions on a scale drawing?
4. How would the answers change if the scale used different units, like centimeters instead of inches?
5. How can you verify the accuracy of a scaled drawing to ensure it matches real-world measurements?

**Tip:** When working with scales, remember that the area changes as the square of the scale factor, so scaling lengths by a factor will change the area by the square of that factor.

Solve scale problems for finding areas based on scale drawings of a grill, an exercise mat, and a driveway.

Solve problems involving scale drawings for a grill, an exercise mat, and a driveway. Learn how to convert scaled dimensions to actual areas and apply scaling factors. Suitable for students in Grades 6-8.

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