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.