the solid figure above is composed of four cubes, each of which has edges of length 1. what is the total surface area (including the bottom) of the solid figure? (Figure here.)
Here’s how I thought about it. First, a cube with edges of length 1 has a surface area of 6—each face has an area of 1.
In the figure, there are 3 cubes you can actually see. Each of those is fully exposed except for one face, so those 3 cubes contribute a surface area of 5 each, for a total of 15.
The last cube that we can’t see in the figure connects with each of the cubes we can see, so it has 3 of its faces covered. That leaves only 3 faces uncovered, so it contributes 3 to the surface area.
Total surface area is 15 + 3 = 18.