To determine the surface area and volume of a box with the shape of a triangular prism, we use the given dimensions. The box has a length ([tex]\(L\)[/tex]) of 25 inches, a width ([tex]\(W\)[/tex]) of 12 inches, and a height ([tex]\(H\)[/tex]) of 5 inches.
### Step-by-Step Solution:
1. Identify the dimensions:
- Length ([tex]\(L\)[/tex]) = 25 inches
- Width ([tex]\(W\)[/tex]) = 12 inches
- Height ([tex]\(H\)[/tex]) = 5 inches
2. Understand the base shape:
- The base of the triangular prism is a right triangle with legs 12 inches and 5 inches.
3. Calculate the area of the triangular base:
- The area [tex]\(A\)[/tex] of a right triangle is given by:
[tex]\[
A = \frac{1}{2} \times \text{base} \times \text{height}
\][/tex]
- Substituting the values:
[tex]\[
A = \frac{1}{2} \times 12 \times 5 = 30 \text{ square inches}
\][/tex]
4. Calculate the volume ([tex]\(V\)[/tex]) of the triangular prism:
- The volume is given by:
[tex]\[
V = \text{Base Area} \times \text{Length}
\][/tex]
- Using the calculated base area of 30 square inches and the length:
[tex]\[
V = 30 \times 25 = 750 \text{ cubic inches}
\][/tex]
Hence, the area of the triangular base is [tex]\( 30 \)[/tex] square inches and the volume of the triangular prism is [tex]\( 750 \)[/tex] cubic inches.
### Summary:
- Base Area of Triangular Prism: [tex]\( 30 \)[/tex] square inches
- Volume of Triangular Prism: [tex]\( 750 \)[/tex] cubic inches
