To find the surface area of this figure, we simply need to take the areas of each of the faces of the figure and add them together.
(To save time, I will only show full work for one face, since the process is the same for all of them and there are quite a few =P )
Very top face: [tex]3mm * 3 mm = 9mm^2[/tex]
Corner side face: [tex]9mm^2[/tex]
Corner top face: [tex]10mm - 3mm = 7mm[/tex]
[tex]7mm * 3mm = 21mm^2[/tex]
( ^ subtract the distance from the side of the whole
figure to where the top face of the base figure appears)
Far right face: [tex]9mm^2[/tex]
Front bottom face: [tex]30mm^2[/tex]
Front top face: [tex]9mm^2[/tex]
Back bottom face: [tex]30mm^2[/tex]
Back top face: [tex]9mm^2[/tex]
Far left face: [tex]18mm^2[/tex]
Very bottom face: [tex]30mm^2[/tex]
Now, we just add all these up.
[tex]30+30+30+21+18+9+9+9+9+9=174mm^2[/tex]
The surface area of the figure is 174 millimeters squared.
Now onto the volume...
This is easier. There are obviously two separate rectangular prisms here which are attached together.
To find volume of a rectangular prism, you just need to multiply length times width times height. We'll do that for both of them, and then add them together.
[tex]3mm * 3mm * 3mm = 27mm^3[/tex]
[tex]10mm * 3mm * 3mm = 90mm^3[/tex]
[tex]27mm^3 + 90mm^3 = 117mm^3[/tex]
The figure has a volume of 117 millimeters squared.
Hope that helped! =)
