Question

What would the surface area of a triangular prism be if the triangular prism was 4 cm in width, 11 cm in length,3 cm in height, and 5cm length of a side.

Answer 1

To calculate the surface area of a triangular prism, you need to find the area of the two triangular bases and the three rectangular sides that make up the prism.

Given:
- Base width (b) of the triangle = 4 cm
- Height (h) of the triangle = 3 cm
- Length (L) of the prism = 11 cm
- One side length of the triangle = 5 cm (assuming this is the hypotenuse)

### Step 1: Calculate the area of the triangular base

The area \(A\) of the triangle can be calculated using the formula:
\[
A = \frac{1}{2} \times \text{base} \times \text{height}
\]

Thus,
\[
A = \frac{1}{2} \times 4 \, \text{cm} \times 3 \, \text{cm} = 6 \, \text{cm}^2
\]

Since there are two triangular bases, the total area of the triangular bases is:
\[
\text{Total area of triangles} = 2 \times A = 2 \times 6 \, \text{cm}^2 = 12 \, \text{cm}^2
\]

### Step 2: Calculate the area of the rectangular sides

The rectangular sides of the prism can be calculated as follows:

1. **Base rectangle (using the base width)**:
\[
A_1 = \text{width} \times \text{length} = 4 \, \text{cm} \times 11 \, \text{cm} = 44 \, \text{cm}^2
\]

2. **Height rectangle (using the height)**:
\[
A_2 = \text{height} \times \text{length} = 3 \, \text{cm} \times 11 \, \text{cm} = 33 \, \text{cm}^2
\]

3. **Side rectangle (using the side length)**:
\[
A_3 = \text{side length} \times \text{length} = 5 \, \text{cm} \times 11 \, \text{cm} = 55 \, \text{cm}^2
\]

### Step 3: Total area of the rectangular sides
Add up the areas of the three rectangular sides:
\[
\text{Total area of rectangles} = A_1 + A_2 + A_3 = 44 \, \text{cm}^2 + 33 \, \text{cm}^2 + 55 \, \text{cm}^2 = 132 \, \text{cm}^2
\]

### Step 4: Calculate the total surface area
Finally, combine the areas of the triangular bases and the rectangular sides:
\[
\text{Total Surface Area} = \text{Total area of triangles} + \text{Total area of rectangles} = 12 \, \text{cm}^2 + 132 \, \text{cm}^2 = 144 \, \text{cm}^2
\]

Thus, the surface area of the triangular prism is **144 cm²**.