Calculating Area and Perimeter of Rectangles, Squares, and Circles

The Organic Chemistry Tutor

This comprehensive math tutorial guides students through calculating the area and perimeter of common geometric shapes, progressing from basic arithmetic to algebraic problem-solving. The video begins with fundamental examples of rectangles and squares, clearly defining area as the two-dimensional space inside a figure and perimeter as the total distance around it. It then transitions into more complex territory, introducing circle calculations involving pi, radius, and diameter. The content advances in difficulty by presenting "working backwards" problems where students must find side lengths given a perimeter, and geometry problems that require the Pythagorean theorem to relate diagonals to side lengths. The final segment demonstrates how to solve word problems where dimensions are defined algebraically, requiring the setup and solution of quadratic equations. This progression allows the video to serve both as an introduction for younger students (in the first half) and a robust review of algebraic geometry for older students. Educators can use this video to differentiate instruction within a single class. The segmented nature allows teachers to assign specific timestamps based on student readiness—using the first half for basic geometry review and the second half for enrichment or algebra application. The step-by-step walkthroughs of word problems are particularly valuable for modeling mathematical thinking and showing how to translate text into mathematical equations.