Composite Solid Surface Area
A composite solid is made by joining two or more 3D shapes. To find its surface area, count only the outside faces that are exposed. Any faces where two solids touch become hidden and should not be included.
Method
- Identify each part of the solid.
Break the figure into familiar shapes such as prisms, cubes, cylinders, or pyramids if possible.
- Find the area of each exposed face.
Use the correct area formulas for rectangles, triangles, circles, or other faces that appear on the outside.
- Add the exposed areas.
Include all visible faces from every part of the solid.
- Subtract hidden faces if needed.
If a face is joined to another solid, remove it from the total because it is not part of the outside surface.
- Simplify your final answer.
Combine like terms, reduce fractions, and write the result with square units.
Check your work
- Make sure every outer face is counted once.
- Make sure no attached face is counted twice.
- Compare the result to the size of the solid; the answer should be reasonable.
Helpful tip
If the figure is hard to manage all at once, compute the surface area of each separate solid first, then adjust for any shared faces.