Question

what is the formula for surface area of a triangular prism and give what each variable repesents

Answer 1

The surface area \( S \) of a triangular prism can be calculated using the following formula:

\[
S = bh + lp + lw
\]

Where:

- \( b \) = base length of the triangular face
- \( h \) = height of the triangular face
- \( l \) = length of the prism (the distance between the two triangular faces)
- \( p \) = perimeter of the triangular face

To elaborate:

1. **\( bh \)** is the area of the triangular face of the prism.
2. **\( lp \)** is the lateral area, which includes the three rectangular sides formed by the sides of the triangle and the length of the prism.
3. **\( lw \)** adds the area of the two triangular bases at both ends of the prism.

In summary, the total surface area consists of the area of the two triangular bases plus the area of the three rectangular lateral faces.

If you want the complete formula with specific reference to perimeter:

\[
S = 2 \times \text{Area of base} + \text{Perimeter of base} \times \text{Length}
\]

This can be expressed as:

\[
S = 2 \times \left(\frac{1}{2} \times b \times h\right) + p \times l
\]

Where \( p \) is the perimeter of the triangle calculated as the sum of its three sides:

\[
p = a_1 + a_2 + a_3
\]

Where \( a_1, a_2, \) and \( a_3 \) are the lengths of the sides of the triangular base.

This breakdown allows you to calculate the total surface area of the triangular prism effectively!