In this lesson, students learn about calculating the area of compound shapes through various formulas. They review the areas of basic shapes such as triangles, rectangles, and parallelograms, emphasizing the need to remember the formulas for effective problem-solving. The instructor provides examples involving a parallelogram and a rectangle to demonstrate how to calculate total area by summing their individual areas. Additionally, the lesson discusses the trapezium, including using the appropriate formula and unit conversions for accurate results.