Question

The figure below is a net for a right rectangular prism. Its surface area is 272 m2 andthe area of some of the faces are filled in below. Find the area of the missing faces,and the missing dimension.

Answer 1

the surface area of a prism is the sum of the areas of all its sides. The surface area is given: 272 m².

We also have the area of 4 of the the sides. The area of the missing ones is the same, since it is a right rectangular prism. So we can write:

`\begin{gathered} 16+16+24+24+A+A=272 \\ 80+2A=272 \\ 2A=272-80 \\ 2A=192 \\ A=96 \end{gathered}`

So the area of the missing faces is 96 m².

Since it is a rectangle of area 96 m² and one side of 8 m, we can find the length of the missing side, "x", by noticing that the area is calculated by the multiplication of the sides:

`\begin{gathered} A=8\cdot x=96 \\ x=(96)/(8) \\ x=12 \end{gathered}`

So, the missing dimension is 12 m.