What is the lateral surface area of the triangular prism below?

Steps to Solve

1. Identify the dimensions for lateral surface area calculation

The lateral surface area (LSA) of a triangular prism can be calculated using the formula:

$$ \text{LSA} = \text{Perimeter of base} \times \text{Height of prism} $$

In this case, we need to determine the perimeter of the triangular base and the height of the prism.

2. Calculate the perimeter of the triangular base

We have a triangular base with sides of lengths 17 cm, 17 cm, and 8 cm. The perimeter (P) is calculated as follows:

$$ P = 17 + 17 + 8 = 42 \text{ cm} $$

3. Determine the height of the prism

The height of the prism is given as 35 cm.

4. Calculate the lateral surface area

Now, use the perimeter and the height to calculate the lateral surface area:

$$ \text{LSA} = P \times \text{Height} $$ $$ \text{LSA} = 42 \times 35 $$

5. Perform the multiplication

Calculating this gives:

$$ \text{LSA} = 1470 \text{ cm}^2 $$

6. Confirm the correct approach for finding the lateral area

The lateral area also consists of the rectangles associated with each side of the triangle (3 sides), where each rectangle has a height equal to the height of the prism and width equal to the sides of the triangle.

The lateral area calculation can also be done this way:

• Area of the first rectangle: $17 \times 35$
• Area of the second rectangle: $17 \times 35$
• Area of the third rectangle: $8 \times 35$

Calculating each gives:

$$ 17 \times 35 = 595 $$ $$ 17 \times 35 = 595 $$ $$ 8 \times 35 = 280 $$

Adding them together:

$$ 595 + 595 + 280 = 1470 \text{ cm}^2 $$