Question

The side of the triangular prism is 5 cm
The length of the triangular prism is 8 cm
The width of the triangular prism is 6 cm

What is the lateral surface area of this triangular prism?
192 cm²

128 cm²

152 cm²

144 cm²

Answer 1

To find the lateral surface area of a triangular prism, you need to consider the areas of the three rectangular faces that connect the corresponding sides of the triangular bases.

The formula for the lateral surface area \( A_L \) of a triangular prism is given by:

\[
A_L = p \times h
\]

where \( p \) is the perimeter of the triangular base and \( h \) is the height (or length) of the prism.

**Step 1: Determine the perimeter of the triangular base.**

The triangular base is defined by its three sides, which in this case are:
- Two sides of 5 cm each (assuming it is an isosceles triangle)
- One side of 6 cm

The perimeter \( p \) is calculated as follows:

\[
p = 5 + 5 + 6 = 16 \text{ cm}
\]

**Step 2: Use the height of the prism.**

Given that the length (height) \( h \) of the prism is 8 cm:

**Step 3: Calculate the lateral surface area.**

We now substitute the values into the formula:

\[
A_L = p \times h = 16 \text{ cm} \times 8 \text{ cm} = 128 \text{ cm}^2
\]

So, the lateral surface area of the triangular prism is **128 cm²**.