Question: Calculate the surface area of the triangular prism below.
16 mm
12 mm
25 mm
33 mm
7 mm
Not drawn accurately
Graph shape: a triangular prism is shown in the center; the triangular cross-section has side lengths 16 mm, 25 mm, and base 33 mm, with a perpendicular height of 12 mm, and the prism length is 7 mm.
1. **State the problem:** Calculate the surface area of a triangular prism with triangular base sides $16$ mm, $25$ mm, and base $33$ mm, height of the triangle $12$ mm, and prism length $7$ mm.
2. **Formula for surface area of a triangular prism:**
$$\text{Surface Area} = 2 \times \text{Area of triangular base} + \text{Perimeter of base} \times \text{Length of prism}$$
3. **Calculate the area of the triangular base:**
The area of a triangle is given by:
$$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$$
Here, base $= 33$ mm and height $= 12$ mm.
$$\text{Area} = \frac{1}{2} \times 33 \times 12 = \frac{1}{2} \times 396 = 198 \text{ mm}^2$$
4. **Calculate the perimeter of the triangular base:**
$$\text{Perimeter} = 16 + 25 + 33 = 74 \text{ mm}$$
5. **Calculate the lateral surface area:**
$$\text{Lateral Surface Area} = \text{Perimeter} \times \text{Length} = 74 \times 7 = 518 \text{ mm}^2$$
6. **Calculate total surface area:**
$$\text{Surface Area} = 2 \times 198 + 518 = 396 + 518 = 914 \text{ mm}^2$$
**Final answer:** The surface area of the triangular prism is $914$ mm$^2$.