Question

a triangular prism is shown it has a base of 14 feet and a height of 25 feet a width of 10 feet and a slant of 25 feet.

Answer 1

To analyze the information about the triangular prism, we can start by breaking down the dimensions provided:

1. **Base (length)**: 14 feet (this is likely the length of the triangular base)
2. **Height (of the triangle)**: 25 feet (this is the height from the base of the triangle to the apex)
3. **Width**: 10 feet (this may refer to the width of the prism or the third dimension transecting the triangular shape)
4. **Slant height**: 25 feet (typically, this would refer to the length of a side of the triangle connecting the base and apex)

From this information, we can calculate aspects like the volume and surface area of the triangular prism.

### Volume of the Triangular Prism

1. **Area of the triangular base**:
The area \( A \) of a triangle can be calculated using the formula:
\[
A = \frac{1}{2} \times \text{base} \times \text{height}
\]
Here, we take the base as 14 feet and the height as 25 feet:
\[
A = \frac{1}{2} \times 14 \times 25 = \frac{1}{2} \times 350 = 175 \text{ square feet}
\]

2. **Volume of the prism**:
The volume \( V \) of a prism is calculated by multiplying the area of the base by the width (length):
\[
V = A \times \text{width} = 175 \times 10 = 1750 \text{ cubic feet}
\]

### Surface Area of the Triangular Prism

To find the surface area, you will need to calculate both the area of the triangular bases and the areas of the three rectangular sides.

1. **Area of the triangular bases**: Since there are two triangular bases:
\[
\text{Area of the two bases} = 2 \times 175 = 350 \text{ square feet}
\]

2. **Area of the three rectangular sides**:
- **Two sides with height and base**:
- Side parallel to the base (14 feet length) and height (25 feet) = \( 14 \times 25 = 350 \text{ square feet} \)
- There are two of these:
\[
2 \times 350 = 700 \text{ square feet}
\]
- **One side with width and height (10 feet width and slant height 25 feet)**:
- Area = \( 10 \times \text{slant height} = 10 \times 25 = 250 \text{ square feet} \)

3. **Total surface area**:
\[
\text{Total surface area} = \text{Area of the bases} + \text{Area of the sides}
\]
Which is:
\[
350 + 700 + 250 = 1300 \text{ square feet}
\]

### Summary
- Volume: **1750 cubic feet**
- Surface Area: **1300 square feet**

Please review the context of the slant height and the dimensions to ensure they are used correctly. The slant height might affect the height of the triangular face if needed for further calculations.