Question

surface area of triangular prism is 524
length of ?
width of of 8
height of 6

Answer 1

To find the length of a triangular prism given its surface area, width, and height, we need to understand the formula for the surface area of a triangular prism. The surface area \( SA \) can be calculated using the formula:

\[
SA = \text{base area} + \text{lateral area}
\]

The base area of the triangular face can be calculated as:

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

The lateral area can be calculated as:

\[
\text{Lateral Area} = \text{perimeter of base} \times \text{length}
\]

Assuming the base of the triangle is the width (8) and the height is (6), the calculations are as follows:

1. **Calculate the base area of the triangle**:
- Base area = \( \frac{1}{2} \times 8 \times 6 = 24 \)

2. **Calculate the perimeter of the triangle**:
- The perimeter of a right triangle (assuming a right triangle is formed with width 8 and height 6) can be calculated using the Pythagorean theorem:
- Hypotenuse \( c = \sqrt{8^2 + 6^2} = \sqrt{64 + 36} = \sqrt{100} = 10 \)
- Perimeter \( = 8 + 6 + 10 = 24 \)

3. **Substituting values into the surface area formula**:
Now, using the surface area formula:

\[
524 = 24 + (24 \times \text{length})
\]
\[
524 - 24 = 24 \times \text{length}
\]
\[
500 = 24 \times \text{length}
\]

4. **Solving for length**:
\[
\text{length} = \frac{500}{24} \approx 20.83
\]

Thus, the length of the triangular prism is approximately **20.83 units**.