Question

A rectangular prism has faces with areas of 20 cm
2
, 10 cm
2
, and 8 cm
2
. What is its total surface area?

Answer 1

Let the dimensions of the rectangular prism be \(x\), \(y\), and \(z\). The areas of the three pairs of opposite faces are given by:

- \(xy = 20 \, \text{cm}^2\)
- \(xz = 10 \, \text{cm}^2\)
- \(yz = 8 \, \text{cm}^2\)

To find the total surface area \(S\) of the rectangular prism, we use the formula:
\[
S = 2(xy + xz + yz)
\]

First, we calculate \(xy + xz + yz\):
\[
xy + xz + yz = 20 + 10 + 8 = 38 \, \text{cm}^2
\]

Now, we calculate the total surface area:
\[
S = 2(xy + xz + yz) = 2(38) = 76 \, \text{cm}^2
\]

Thus, the total surface area of the rectangular prism is
\[
\boxed{76 \, \text{cm}^2}
\]