How to Find the Area of a Shaded Region with Inscribed Squares

The Organic Chemistry Tutor

This math tutorial guides viewers through solving a geometry problem involving a square inscribed within a larger square. The goal is to calculate the area of the shaded region, which consists of the four corners remaining between the two squares. The video breaks down the problem using a logical subtraction strategy: calculating the total area of the large square and subtracting the area of the inner inscribed square. Key mathematical concepts explored include the area formula for squares, the definition of midpoints, and the Pythagorean theorem. The narrator demonstrates how to identify right triangles within the geometry of the shape to calculate the missing side length of the inner square. The video also touches upon simplifying radicals (square roots) when solving for side lengths, though it notes that squaring the radical later simplifies the process. This video is a valuable resource for middle and high school geometry classrooms. It models clear problem-solving heuristics—specifically breaking complex shapes into simpler components—and provides a practical application for the Pythagorean theorem beyond standard triangle problems. It is particularly useful for visual learners, as it explicitly draws out the triangles and labels dimensions to make the abstract calculations concrete.