Question

Determine the total surface area of the triangular prism.
11 cm
5cm
3cm
4cm

(5 points)
Area of each triangular face =
square centimeters

Area of the smallest rectangular face =
square centimeters

Area of the middle rectangular face =
square centimeters

Area of the largest rectangular face =
square centimeters

TOTAL Surface Area of the Triangular Prism =
square centimeters

Answer 1

To determine the total surface area of a triangular prism, we need to calculate the areas of its triangular faces and rectangular faces based on the measurements provided:

1. **Area of each triangular face**:
We can calculate the area of the triangular face using the formula for the area of a triangle:

\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]

Given:
- Base = 5 cm
- Height = 4 cm

\[
\text{Area of the triangular face} = \frac{1}{2} \times 5 \, \text{cm} \times 4 \, \text{cm} = \frac{1}{2} \times 20 \, \text{cm}^2 = 10 \, \text{cm}^2
\]

Since the prism has two triangular faces, the total area of the triangular faces is:
\[
2 \times 10 \, \text{cm}^2 = 20 \, \text{cm}^2
\]

2. **Area of the rectangular faces**:
The prism has three rectangular faces. We can calculate the area of each rectangular face using the formula:

\[
\text{Area} = \text{length} \times \text{width}
\]

Assuming:
- The smallest rectangular face has a height of 3 cm (this face corresponds to the edge of 3 cm of the triangle)
- The middle rectangular face corresponds to the edge of 4 cm
- The largest rectangular face corresponds to the edge of 5 cm

- **Smallest rectangular face** (height 3 cm, base 5 cm):
\[
\text{Area} = 5 \, \text{cm} \times 3 \, \text{cm} = 15 \, \text{cm}^2
\]

- **Middle rectangular face** (height 4 cm, base 5 cm):
\[
\text{Area} = 5 \, \text{cm} \times 4 \, \text{cm} = 20 \, \text{cm}^2
\]

- **Largest rectangular face** (height 4 cm, base 11 cm):
\[
\text{Area} = 11 \, \text{cm} \times 4 \, \text{cm} = 44 \, \text{cm}^2
\]

3. **Total Surface Area of the Triangular Prism**:
Now, we can add the areas of the triangular faces and the rectangular faces together:

- Total area of triangular faces = 20 cm²
- Area of the smallest rectangular face = 15 cm²
- Area of the middle rectangular face = 20 cm²
- Area of the largest rectangular face = 44 cm²

\[
\text{Total Surface Area} = 20 \, \text{cm}^2 + 15 \, \text{cm}^2 + 20 \, \text{cm}^2 + 44 \, \text{cm}^2 = 99 \, \text{cm}^2
\]

Thus, the final answers are:

- Area of each triangular face = **10 cm²**
- Area of the smallest rectangular face = **15 cm²**
- Area of the middle rectangular face = **20 cm²**
- Area of the largest rectangular face = **44 cm²**
- TOTAL Surface Area of the Triangular Prism = **99 cm²**