https://file.aiquickdraw.com/mathbot/file/1729700162285t26435bv.jpg

The image depicts a triangular prism. To calculate the surface area of this prism, we need to find the area of its two triangular faces and the three rectangular faces. Let's break it down.

### 1. Triangular Faces
The triangle has a height of 15 cm and a base of 16 cm. The area \(A_{\text{triangle}}\) of each triangular face is given by:
\[
A_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height}
\]
\[
A_{\text{triangle}} = \frac{1}{2} \times 16 \, \text{cm} \times 15 \, \text{cm} = 120 \, \text{cm}^2
\]
Since there are two triangular faces, the total area for the triangles is:
\[
2 \times 120 \, \text{cm}^2 = 240 \, \text{cm}^2
\]

### 2. Rectangular Faces
There are three rectangular faces:
- One face with dimensions \(16 \, \text{cm} \times 17 \, \text{cm}\)
- One face with dimensions \(12 \, \text{cm} \times 17 \, \text{cm}\)
- One face with dimensions \(15 \, \text{cm} \times 17 \, \text{cm}\)

The areas of these rectangles are:
\[
A_{\text{rect1}} = 16 \times 17 = 272 \, \text{cm}^2
\]
\[
A_{\text{rect2}} = 12 \times 17 = 204 \, \text{cm}^2
\]
\[
A_{\text{rect3}} = 15 \times 17 = 255 \, \text{cm}^2
\]

### 3. Total Surface Area
The total surface area is the sum of the areas of the two triangular faces and the three rectangular faces:
\[
A_{\text{total}} = 240 \, \text{cm}^2 + 272 \, \text{cm}^2 + 204 \, \text{cm}^2 + 255 \, \text{cm}^2 = 971 \, \text{cm}^2
\]

Thus, the surface area of the triangular prism is **971 cm²**.

Would you like more details or have any questions?

### Related questions:
1. How would the surface area change if the height of the triangle increased by 5 cm?
2. What would be the volume of this prism if the length of the prism was 20 cm?
3. How do you calculate the lateral surface area of a triangular prism?
4. What is the relationship between surface area and volume in prisms?
5. How would you calculate the surface area if the triangular base was an isosceles triangle?

### Tip:
When calculating the surface area of prisms, always separate triangular faces and rectangular faces for easier management of the different dimensions.

What is the surface area of this triangular prism?

Learn how to find the surface area of a triangular prism with a base of 16 cm, height of 15 cm, and side lengths of 17 cm. This step-by-step solution includes finding the area of triangular and rectangular faces for students in Grades 6-8.

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