This leads to finding out which type of triangle encloses the largest area and then to finding rules for the areas of the three shapes for a fixed perimeter. The question: - For a perimeter of fixed length, which shape, a triangle, a square or a circle, will enclose the largest area? - can provide the stimulus for this exploration. Area of Equilateral Triangle, Square and Circle for Fixed Perimeter The rule for the quadratic function can be found by use of the Theorem of Pythagoras.ĪnnulusAreaProbSheet (pdf) - student sheet with a statement of the problem and a diagramĪnnulusAreaGSPSketch (zipped gsp) - a Geometer's Sketchpad sketch with a page giving the problem and a diagram that can be changed, a second page for collecting and plotting data from the diagram, a third page for exploring the functional relationship between variables in the problem, and a final page showing the function rule link buttons can be used to move through the pages in sequence. This can initiate an exploration of the relationship between the area of an annulus and the length of the chord of the larger circle that is tangent to the inner circle of the annulus. This problem uses the need for a gardener to find the area of circular garden path surrounding a circular pool as its real-life context. Quadratic Functions and Equations: An Overview (zipped ppt) Annulus Area Problem In the following Power Point presentation Professor Kaye Stacey provides an overview of the key topics and themes that make up the study of Quadratic Funtions and Equations in secondary school mathematics. You might also look at our section on surds Transformations of the Graph of a Quadratic Function Ritemaths - Real World problems and Information Technology Enhancing MathematicsĪrea of Equilateral Triangle, Square and Circle for a Fixed Perimeter
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