To solve this problem, we will use the provided dimensions of the prism (length, width, and height) to find the unknown side lengths and then calculate the lateral surface area and the total surface area.
Let's assume the dimensions of the rectangular prism are:
- Length (L) = 9 m (the longer side)
- Width (W) = 6 m (the shorter side)
- Height (H) = 2 m
Now, we can find the side lengths for the net.
(a) Find the following side lengths for the net:
From the net of a rectangular prism, we can label the sides as follows:
- A: Height of the prism (H) = 2 m
- B: Width (W) = 6 m
- C: Length (L) = 9 m
- D: Height (H) = 2 m (again, as it appears on the sides of the net)
So, we have:
- A = 2 m
- B = 6 m
- C = 9 m
- D = 2 m
(b) Use the net to find the lateral surface area of the prism. Neither the top nor bottom is included.
The lateral surface area (LSA) of a rectangular prism is given by the formula:
\[ \text{LSA} = 2 \times (H \times L + H \times W) \]
Using the values we have:
- H = 2 m
- L = 9 m
- W = 6 m
Calculating the lateral surface area:
\[ \text{LSA} = 2 \times (2 \times 9 + 2 \times 6) \] \[ \text{LSA} = 2 \times (18 + 12) \] \[ \text{LSA} = 2 \times 30 \] \[ \text{LSA} = 60 , m^2 \]
(c) Use the net to find the total surface area of the prism.
The total surface area (TSA) of a rectangular prism is given by the formula:
\[ \text{TSA} = 2 \times (L \times W + L \times H + W \times H) \]
Using the same values:
- L = 9 m
- W = 6 m
- H = 2 m
Calculating the total surface area:
\[ \text{TSA} = 2 \times (9 \times 6 + 9 \times 2 + 6 \times 2) \] \[ \text{TSA} = 2 \times (54 + 18 + 12) \] \[ \text{TSA} = 2 \times 84 \] \[ \text{TSA} = 168 , m^2 \]
Summary of Results:
- (a)
- A = 2 m
- B = 6 m
- C = 9 m
- D = 2 m
- (b) Lateral Surface Area = 60 m²
- (c) Total Surface Area = 168 m²