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 \[ \boxed{76 , \text{cm}^2} \]