Apply area formulas for triangles, parallelograms, trapezoids, regular polygons, circles, and sectors, including composite figures.
Area formulas for polygons build on one core idea: a base and a height PERPENDICULAR to that base. A triangle's area is (1/2) * base * height; a parallelogram's is base * height (no 1/2, since a parallelogram is really two triangles); a trapezoid's is (1/2) * (base1 + base2) * height, averaging its two parallel bases first. A regular polygon's area is (1/2) * perimeter * apothem, where the apothem is the perpendicular distance from the center to a side -- this comes from splitting the polygon into congruent triangles from the center.
A circle's area is pi * r^2, and a sector (a pie-slice piece bounded by two radii and an arc) takes just a fraction of that: area of sector = (arc measure / 360) * pi * r^2. For any composite figure, break it into polygons and circle-pieces you already know how to handle, then add the pieces together -- or subtract, if one shape is a hole cut from another. One more fact from the similarity unit: if two figures are similar with scale factor k, their AREAS have ratio k^2, not k -- doubling every side quadruples the area.
Mastery looks like: They correctly apply the area formulas for triangles, parallelograms, trapezoids, regular polygons, circles, and sectors, and combine or subtract areas for composite figures.
Common stumbles: Forgetting the 1/2 in the triangle, trapezoid, or regular-polygon area formulas; using the arc measure directly as an area instead of first converting it to a fraction of 360.