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This shape appears to be a triangular prism based on the right triangle at the base, where the dimensions are provided: 11 cm, 13 cm, and 7 cm. Let's calculate the total surface area step by step.

### Step 1: Calculate the area of the two triangular bases
The triangle is a right-angled triangle with legs 11 cm and 7 cm, and the hypotenuse is 13 cm (since \( 11^2 + 7^2 = 13^2 \)).

- The area \( A_{\text{triangle}} \) of one triangle is:
  \[
  A_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 11 \times 7 = 38.5 \, \text{cm}^2
  \]

Since there are two triangular faces, the total area for both triangles is:
\[
A_{\text{triangles}} = 2 \times 38.5 = 77 \, \text{cm}^2
\]

### Step 2: Calculate the areas of the three rectangular lateral faces
The dimensions for the lateral faces are based on the lengths of the sides of the triangle and the prism's height (17 cm):

- The area of the rectangle along the 11 cm side:
  \[
  A_{\text{11-side}} = 11 \times 17 = 187 \, \text{cm}^2
  \]

- The area of the rectangle along the 7 cm side:
  \[
  A_{\text{7-side}} = 7 \times 17 = 119 \, \text{cm}^2
  \]

- The area of the rectangle along the 13 cm side (hypotenuse):
  \[
  A_{\text{13-side}} = 13 \times 17 = 221 \, \text{cm}^2
  \]

### Step 3: Add up all the areas
- Total lateral surface area:
  \[
  A_{\text{lateral}} = 187 + 119 + 221 = 527 \, \text{cm}^2
  \]

- Total surface area:
  \[
  A_{\text{total}} = A_{\text{triangles}} + A_{\text{lateral}} = 77 + 527 = 604 \, \text{cm}^2
  \]

Thus, the total surface area of the triangular prism is **604 cm²**.

Would you like more details or have any questions?

### Relative questions:
1. How would the total surface area change if the prism height were doubled?
2. Can you calculate the volume of this prism?
3. What formula applies to find the lateral surface area of a cylinder?
4. How would you approach finding the surface area of a cube instead?
5. How does the surface area formula for a pyramid differ from that of a prism?

**Tip:** When calculating surface areas, always break down the shape into its individual faces and calculate the area of each part before summing them up.

Find the total surface area of a triangular prism with triangle sides 11 cm, 7 cm, 13 cm and a prism height of 17 cm.

Find out how to calculate the total surface area of a triangular prism with base dimensions of 11 cm, 7 cm, 13 cm, and a height of 17 cm. This guide covers essential geometry concepts, including calculating the areas of triangles and rectangular faces. Suitable for students in Grades 7-9.

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