Question

Where can I solve and get the total area of the surface ?

Answer 1

In order to calculate the total surface area of this figure, let's consider the following views:

From above: 2 rectangles, one with dimensions 8 and 6 and one with dimensions 12 and 6.

From below: 1 rectangle with dimensions 20 and 6.

From the right: 2 rectangles, both with dimensions 6 and 4.

From the left: 1 rectangle with dimensions 6 and 8.

From the front and back: 2 composite figures, made by 2 rectangles each, one with dimensions 8 and 4 and one with dimensions 20 and 4.

So the total surface area is:

`\begin{gathered} S=(8\cdot6+12\cdot6)+(20\cdot6)+2\cdot(6\cdot4)+(6\cdot8)+2\cdot(8\cdot4+20\cdot4) \\ S=120+120+48+48+224 \\ S=560\text{ cm}^2 \end{gathered}`

Therefore the surface area of the figure is equal to 560 cm².