To calculate the surface area of the triangular prism, we will sum up the areas of all its faces: two triangular bases and three rectangular sides.

Step 1: Calculate the area of one triangular base

The base of the triangle is 23 cm, and its height is 10 cm. The area of a triangle is given by:

$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$

$\text{Area of one triangle} = \frac{1}{2} \times 23 \times 10 = 115 \, \text{cm}^2$

Since there are two identical triangular bases:

$\text{Total area of triangular bases} = 2 \times 115 = 230 \, \text{cm}^2$

Step 2: Calculate the area of the three rectangular faces

The dimensions for the rectangular faces are:

• Rectangle 1 (adjacent to side 24 cm): $\text{Area} = 24 \times 26 = 624 \, \text{cm}^2$
• Rectangle 2 (adjacent to side 23 cm): $\text{Area} = 23 \times 26 = 598 \, \text{cm}^2$
• Rectangle 3 (adjacent to side 10 cm): $\text{Area} = 10 \times 26 = 260 \, \text{cm}^2$

Step 3: Add the areas of all faces

Now, sum up the areas:

$\text{Surface Area} = \text{Area of triangular bases} + \text{Area of rectangular faces}$

$\text{Surface Area} = 230 + 624 + 598 + 260 = 1712 \, \text{cm}^2$

Final Answer:

The surface area of the triangular prism is:

$\boxed{1712 \, \text{cm}^2}$

Would you like more details or have questions?

Related Questions:

1. How is the formula for a triangular prism's surface area derived?
2. What is the volume of this triangular prism?
3. How would the surface area change if the height of the prism increased?
4. Can you calculate the lateral area (only the rectangular faces)?
5. What are the units of surface area, and why are they squared?

Tip:

Always verify each dimension when calculating the areas to ensure accuracy. Misreading values is a common mistake!