Question

Please help me with the question below (also please explain).

Answer 1

The surface area of a rectangular prism with sides a, b and c is:

`S=2(ab+ac+bc)`

The composite figure is made of two rectangular prisms, whose sides are 3in*3in*11in and 6in*8in*11in. However, notice that one face of the blue prism is touching the surface of the orange prism, hiding a portion of the surface area equivalent to two times the area of a 3in*11in rectangle (it is two times because one is due to the blue surface that is hidden and the other is for the corresponding orange surface, also hidden).

Then, to find the area of the composite figure, add the surface area of each rectangular prism and then subtract 2*3in*11in.

Blue prism:

`S_B=2(3in*3in+3in*11in+3in*11in)=150in^2`

Orange prism:

`S_O=2(6in*8in+6in*11in+8in*11in)=404in^2`

Composite figure:

`\begin{gathered} S=S_B+S_O-2(3in*11in) \\ \\ =150in^2+404in^2-66in^2 \\ \\ =488in^2 \end{gathered}`

Therefore, the surface area of the composite figure is 488 in^2.