For the number of trapezoids, you have ones made up of one horizontal layer. two layers, and three layers.
How many of each in total? Record this number.
For a given horizontal layer, you can join four adjacent sections to form one trapezoid, you can join three adjacent
sections in how many ways to form shorter trapezoids, etc. How many total trapezoids can you form in one layer
using this manner? Do it for all of the horizontal layers. Record this second number.
Multiply the two recorded numbers to get the total number of trapezoids. It can be easier to do/practice with a
figure that has fewer rows and fewer slanted line segments.
For the numbers of triangles, this time you have four rows from which to use to make triangles. The height of a
triangle varies according as you add a row beneath the topmost row. Also, the number of triangles also increases
as you move sideways. You could start with the entire figure as one triangle. Or, look at the slanted line segments.
There are four adjacent sections. You could choose one of the four. Look at the three overlapping sections of two
sections. You could choose one of those. Etc.
You should show your work and attempts here, based on some of the hints above.
