Students will use the volume and surface area formulas they know, to find the volume and surface area of composite figures. Students will see problems where one figure is combined with another, as well as problems where one figure has been removed from another. As an example of the former, a right rectangular prism with a rounded edge. As an example of the latter, a right rectangular prism with a hole drilled through. Here's a lesson and practice. And here's a couple more problems.
Concude by giving your students this challenge:
The L shape below consists of two overlapping congruent rectangles. If the perimeter of the L shape is 40 cm, what can we say about the length and width of each rectangle?
Here's the solution: Let \(w\) be the width for one of the rectangles, and \(h\) the height, with \(w \gt h.\) By rearranging the line segments which form the boundary of the L shape, we can see it has perimeter \(4w.\) Thus, we know \(4w = 40\) and therefore \(w = 4.\) We can't say anything about \(h.\) If instead, \(w \lt h,\) then \(h = 4,\) and we can't say anything about \(w.\) If \(w = h,\) then we no longer have an L shape, but a square. Since the problem specifies an L shape, this can't be the case.
Note: This is the NRICH problem L-emental. I copied it because I wanted to provide a more detailed solution.