Crystal knows that the surface areas of the front, top, and right faces of a prism add to 20 cm². How can she find the total surface area of the prism? Explain.
If the surface areas of the front, top, and right faces of a prism add to 20 cm², then we can assume that these are the only three faces that are visible when the prism is in its normal position. Therefore, we can find the surface area of the entire prism by doubling the surface area of these three faces (since there are two of each face in the prism).
In other words, if we let A be the surface area of the front face, B be the surface area of the top face, and C be the surface area of the right face, then the total surface area of the prism would be:
2A + 2B + 2C
Substituting in the given value of 20 cm², we get:
2A + 2B + 2C = 20
Dividing both sides by 2, we get:
A + B + C = 10
This tells us that the sum of the surface areas of the front, top, and right faces is 10 cm². To find the total surface area of the prism, we simply need to double this sum:
2(A + B + C) = 2(10) = 20
Therefore, the total surface area of the prism is 20 cm².