Question

Find the surface area of the composite figure.

5 cm
6 cm
20 cm
4 cm
5 cm 4 cm
SA =
12 cm
-6 cm
[?] cm²

Answer 1

`644cm^2`

Explanation:

First we'll work out the surface area of the pink figure.

That's the area of the two 5 by 6 rectangles on the top and bottom, plus the area of the two 5 by 20 and two 6 by 20 rectangles on the sides.

However, we note that the purple figure is blocking out a 6 by 12 section on the pink figure, so we'll need to subtract this.

The above works out to
`2*(30+100+120)-72=428 cm^2`.

Then we'll work out the surface area of the purple figure.

This will be the area of the two 4 by 6 rectangles at the top and bottom, plus the area of the two 4 by 12 and one 6 by 12 rectangles on the sides. Note that there's only one 6 by 12 rectangle because the other face is joined to the pink figure, so it's blocked out.

That's
`2*(24+48)+72=216cm^2`.

So the total surface area is
`428+216=644cm^2`.