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Calculate the area of this room, and the length of the missing wall

I have viewed the image you uploaded. Let's break down the calculations for the area of the room and the missing wall length based on the dimensions provided in the image.

### Step 1: Determine the shape and dimensions
The room appears to be a composite shape, consisting of a rectangular section with a right-angled triangle attached to it.

### Given dimensions:
1. **Rectangle part:**
   - Width = 10 ft (horizontal segment at the bottom)
   - Height = 6 ft (vertical segment on the right side)

2. **Right-angled triangle:**
   - Base = 2 ft (horizontal segment at the top right)
   - Height = 2 ft (vertical segment on the top left)
   - Hypotenuse = the inclined line (not provided directly)

### Step 2: Calculate the missing wall length
The missing wall length corresponds to the hypotenuse of the right-angled triangle.

Using the Pythagorean theorem:
\[
\text{Hypotenuse} = \sqrt{\text{Base}^2 + \text{Height}^2}
\]
\[
\text{Hypotenuse} = \sqrt{2^2 + 2^2} = \sqrt{4 + 4} = \sqrt{8} = 2\sqrt{2} \text{ ft} \approx 2.83 \text{ ft}
\]

### Step 3: Calculate the area of the room
1. **Area of the rectangular part:**
   \[
   \text{Area}_{\text{rectangle}} = \text{Width} \times \text{Height} = 10 \times 6 = 60 \text{ square feet}
   \]

2. **Area of the triangular part:**
   \[
   \text{Area}_{\text{triangle}} = \frac{1}{2} \times \text{Base} \times \text{Height} = \frac{1}{2} \times 2 \times 2 = 2 \text{ square feet}
   \]

3. **Total Area of the room:**
   \[
   \text{Total Area} = \text{Area}_{\text{rectangle}} + \text{Area}_{\text{triangle}} = 60 + 2 = 62 \text{ square feet}
   \]

### Final Answer:
- **Total area of the room:** 62 square feet.
- **Length of the missing wall (hypotenuse):** 2.83 feet.

Would you like any additional details or have any further questions? Here are some related questions that might be of interest:

1. How does the Pythagorean theorem apply to right-angled triangles?
2. What are some real-world applications of calculating the area of composite shapes?
3. How would the area change if the room had different dimensions?
4. What is the significance of precision in calculating areas in construction?
5. How could we calculate the perimeter of this room?

**Tip:** Always double-check measurements when calculating areas or perimeters, as small errors can significantly impact the final result.

Learn how to calculate the area of a room composed of a rectangle and a right-angled triangle, and find the length of the missing wall using the Pythagorean theorem. Detailed step-by-step solution provided. Suitable for Grades 6-8 students.

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