Maximizing the Area of Some Geometric Figures of Fixed Perimeter

figure

rectangle

length of base, x

x = 2

area = 6

This Demonstration illustrates a common type of max-min problem from a Calculus I course—that of finding the maximum area of a geometric figure of fixed perimeter. The figures available are a rectangle, a right triangle, an isosceles triangle, a Norman window (a rectangle topped by a semicircle), and a "side view of a house" (a rectangle topped by an equilateral triangle). The perimeter is 10 units for each figure.