Methods for Finding the Area of Irregular Figures

• Sections:
• Total Articles: 13
• Cost: Free
• Duration: 12 hours

Average time it takes to complete the course and exercises.

This mini-course aims to address the need for practical solutions in finding the area of irregular shapes, specifically targeting high school students interested in entering the trades or college-level mathematics courses focused on real-world applications. Current courses offered in the grade-12 Ontario curriculum lack a realistic approach to determining the area of irregular figures (e.g. a maple leaf or an outline of a rock). This course fills that gap by introducing three distinct methods for approximating the area of unusual shapes, namely the geometric method, the offset method, and Simpson’s rule. The geometric method involves approximating the irregular space as a polygon and dividing it into non-overlapping triangles, utilizing Heron’s formula to calculate their areas. The offset method, based in calculus, subdivides the shape into a series of trapezoids to estimate the area. Lastly, Simpson’s rule, another calculus-based technique, offers improved accuracy compared to the offset method by using parabolic segments. By equipping students with these skills, they will develop a stronger foundation in applied mathematics, enabling them to tackle real-world challenges and better prepare for future endeavors in trades or higher education.

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