Question

the table shows the area of each of the faces. what is the surface area?

face | area
a | 6 square units
b | 8 square units
c | 12 square units
opposite a | 6 square units
opposite b | 8 square units
opposite c | 12 square units

the surface area of the prism is \boxed{} square units.

Explanation:

Step1: Recall the formula for the surface area of a prism

The surface area of a prism is the sum of the areas of all its faces. For a rectangular prism (or any prism with pairs of opposite faces), we sum the area of each face and its opposite.

Step2: Sum the areas of all faces

We have three pairs of faces:

• Face A and Opposite A: \(6 + 6 = 12\) square units
• Face B and Opposite B: \(8 + 8 = 16\) square units
• Face C and Opposite C: \(12 + 12 = 24\) square units

Step3: Calculate the total surface area

Now, add these sums together: \(12 + 16 + 24 = 52\) square units.

Answer:

52