What is the surface area of the right triangular prism described?

What is the surface area of the right triangular prism described?

• A. 84
• B. 92
• C. 96
• D. 120

Answer: (A)

To find the surface area of a right triangular prism, it is important to understand how the surface area is calculated. The surface area is comprised of two components: the areas of the triangular bases and the area of the three rectangular lateral faces. First, calculate the area of the triangular base. If the base of the triangle has a certain length and height, the area is determined by the formula: \[ Area_{\triangle} = \frac{1}{2} \times \text{base} \times \text{height} \] Since there are two triangular bases in a prism, the total area of the triangular bases is: \[ 2 \times Area_{\triangle} \] Next, the lateral faces are rectangles formed by multiplying the lengths of the sides of the triangle by the height (or length) of the prism. If the side lengths of the triangle are \(a\), \(b\), and \(c\), the areas of the three rectangular faces are as follows: 1. Rectangle opposite the base - \(a \times h\) 2. Rectangle opposite the height - \(b \times h\) 3. Rectangle opposite the other side - \(c \times h\) The total area of the rectangular lateral faces

To find the surface area of a right triangular prism, it is important to understand how the surface area is calculated. The surface area is comprised of two components: the areas of the triangular bases and the area of the three rectangular lateral faces.

First, calculate the area of the triangular base. If the base of the triangle has a certain length and height, the area is determined by the formula:

[ Area_{\triangle} = \frac{1}{2} \times \text{base} \times \text{height} ]

Since there are two triangular bases in a prism, the total area of the triangular bases is:

[ 2 \times Area_{\triangle} ]

Next, the lateral faces are rectangles formed by multiplying the lengths of the sides of the triangle by the height (or length) of the prism. If the side lengths of the triangle are (a), (b), and (c), the areas of the three rectangular faces are as follows:

1. Rectangle opposite the base - (a \times h)

2. Rectangle opposite the height - (b \times h)

3. Rectangle opposite the other side - (c \times h)

The total area of the rectangular lateral faces