How to Find the Area of Composite Figures

Miacademy & MiaPrep Learning Channel

This instructional math video guides students through the process of calculating the area of composite figures—complex shapes formed by combining standard geometric shapes like rectangles, triangles, and trapezoids. The narrator, Justin, breaks down the problem-solving strategy into three clear steps: decomposing the complex figure into known standard shapes, calculating the area of each individual shape, and then combining those areas to find the total. The lesson emphasizes that there are often multiple valid ways to decompose a figure. The video explores key themes such as spatial visualization, the use of geometry formulas, and strategies for finding missing side lengths using deduction and subtraction. It explicitly addresses two types of problems: additive area problems (summing up shapes) and subtractive area problems (where a shape, like a semicircle, is 'cut out' of the figure). The video also clarifies assumptions students can make within the context of the lesson, such as assuming lines that appear perpendicular or parallel are so. This resource is highly valuable for middle school geometry classrooms as it provides a structured approach to a common stumbling block for students: seeing the 'hidden' shapes within a complex polygon. By walking through two distinct examples step-by-step—including finding tricky missing dimensions—it models the critical thinking required for solving geometry problems. It serves as an excellent direct instruction tool or a review resource for students learning to apply area formulas in more complex contexts.