This standard mentions “special quadrilaterals” but doesn’t spell out what they are (apart from parallelograms mentioned in the grade level introduction). I guess the fact that polygons are mentioned in a general way means that anything is fair game. Is the intention that students learn particular formulas for the special quads? Or is it more that students should be able to reason their way through any polygon if they understand area for rectangles and triangles?
Here’s a quote from the K-6 Geometry Progression (page 19): “Also building on their knowledge of composition and decomposition, students decompose rectilinear polygons into rectangles, and decompose special quadrilaterals and other polygons into triangles and other shapes, using such decompositions to determine their areas, and justifying and finding relationships among the formulas for the areas of different polygons.”
The standard asks students to find areas through composition and decomposition. To me, this makes formulas less “things to know” and more “things to justify and connect”.
I’ve taken this to mean that students should be able to find the area of anything by composing and decomposing. If we start giving a formula for everything, it’s going to turn into a memorization task and the conceptual understanding will be lost. Outside of formulas for rectangles and triangles/parallelograms (justified through decomposition/composition), I think other formulas would be more distracting than helpful at this level.