To calculate the surface area of the prism using the given dimensions, we first need to determine the shape of the prism and identify which dimensions correspond to which parts.
Since you mentioned a net and provided four numbers (5 mm, 6 mm, 8 mm, 4 mm), we can assume that these dimensions correspond to the lengths of the edges of a rectangular prism or a triangular prism.
If it's a Rectangular Prism:
- Assume the dimensions are the lengths of the edges of a rectangular prism where:
- length (l) = 8 mm
- width (w) = 6 mm
- height (h) = 5 mm
The formula to find the surface area \( A \) of a rectangular prism is: \[ A = 2(lw + lh + wh) \] Plugging in the values: \[ A = 2(8 \cdot 6 + 8 \cdot 5 + 6 \cdot 5) \] \[ A = 2(48 + 40 + 30) \] \[ A = 2(118) = 236 , \text{mm}^2 \]
If it's a Triangular Prism:
If you interpret these measurements as the base of the triangular prism:
- Assume triangle base of dimensions:
- Base (b) = 6 mm
- Height (h) = 4 mm
- And the length of the prism (l) = 8 mm.
-
First, calculate the area of the triangular base: \[ \text{Area}_{triangle} = \frac{1}{2} \times b \times h = \frac{1}{2} \times 6 \times 4 = 12 , \text{mm}^2 \]
-
Then the area of the three rectangular sides (since a triangular prism has 3 rectangular faces in addition to 2 triangular bases):
- The sides would be:
- Rectangular side 1 = l × h = 8 mm × 5 mm = 40 mm²
- Rectangular side 2 = b × l = 6 mm × 8 mm = 48 mm²
- Rectangular side 3 = l × height of triangular prism side = 8 mm × 4 mm = 32 mm²
- The sides would be:
-
Surface area calculation: \[ A = 2 \times \text{Area}{triangle} + \text{Area}{rectangles} = 2 \times 12 + 40 + 48 + 32 \] \[ A = 24 + 40 + 48 + 32 = 144 , \text{mm}^2 \]
Please clarify the shape of the prism or confirm specific dimension assignments if this does not match what you expected.