https://file.aiquickdraw.com/mathbot/file/1726726656596aq9zm3kh.jpg

The image provided shows a tent design, and the task is to calculate:

a. **The surface area of the tent**  
b. **The cost of purchasing the fabric, given that the fabric costs Rp100,000 per square meter**  

### Step-by-Step Calculation:

#### **a. Surface Area of the Tent**

The tent is shaped like a combination of a rectangular base and a pyramid-like roof. Based on the given dimensions:

- **Base dimensions:** 8m by 8m (a square base).
- **Height of the vertical walls:** 2m.
- **Slant height of the roof (side triangle faces):** 5m.

##### 1. **Area of the four vertical walls:**
These walls are rectangular, and their height is 2 meters. For each side:
- **2 vertical walls (width of 8m):**  
  Area of each = \( 8 \, \text{m} \times 2 \, \text{m} = 16 \, \text{m}^2 \)  
  Total for both walls = \( 16 \times 2 = 32 \, \text{m}^2 \)
  
- **2 vertical walls (width of 8m):**  
  Area of each = \( 8 \, \text{m} \times 2 \, \text{m} = 16 \, \text{m}^2 \)  
  Total for both walls = \( 16 \times 2 = 32 \, \text{m}^2 \)

Total for all vertical walls = \( 32 + 32 = 64 \, \text{m}^2 \).

##### 2. **Area of the roof:**
The roof consists of 4 triangular faces. Each triangle has:
- **Base:** 8 meters  
- **Height (slant height):** 5 meters  

The area of one triangular face = \( \frac{1}{2} \times 8 \, \text{m} \times 5 \, \text{m} = 20 \, \text{m}^2 \)

There are 4 such triangular faces, so total area of the roof = \( 4 \times 20 = 80 \, \text{m}^2 \).

##### 3. **Total surface area of the tent:**

Total surface area = area of vertical walls + area of the roof  
= \( 64 + 80 = 144 \, \text{m}^2 \).

#### **b. Cost of purchasing the fabric**

Given the fabric costs **Rp100,000 per square meter**, the total cost will be:

\[
\text{Cost} = 144 \, \text{m}^2 \times 100,000 \, \text{Rp/m}^2 = 14,400,000 \, \text{Rp}
\]

### Final Answer:
- a. **Surface area of the tent:** 144 m²  
- b. **Cost of purchasing fabric:** Rp 14,400,000

Would you like more details on any step? 

Here are 5 related questions you might find helpful:
1. How do you calculate the surface area of a triangle with different dimensions?
2. How would the calculation change if the tent had a floor?
3. What is the difference between slant height and vertical height in a pyramid?
4. How can we calculate the fabric cost if the price changes?
5. How can we determine the amount of fabric if a seam allowance is needed?

**Tip:** Always double-check the slant height and base dimensions when calculating the surface area of pyramidal structures.

Paman merencanakan membuat tenda tanpa alas seperti pada gambar dengan harga kain Rp100.000, per m², tentukan a. Luas tenda b. Biaya pembelian kain.

Learn how to calculate the surface area of a tent and determine the fabric cost given the price per square meter. This problem involves geometry concepts, such as calculating the area of rectangular walls and triangular roof sections. Suitable for students in Grades 7-9.

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