Squaring off with area

The Problem A rectangle is to have a perimeter of 36 feet and the greatest area possible. What are the dimensions of the rectangle that has the greatest 

You see that the area values start decreasing when you pass the point where the rectangle is a square. A rectangle that s actually a square has the greatest possible area for a given perimeter. This statement is most easily proved using calculus. For now, the demonstration with the table should suffice. 

The house-shaped hexagon on the left is a rectangle topped by a trapezoid. Add the two areas together to get the total area. The area of the rectangle is 

12 x 4 = 48 square inches. The area of a trapezoid is A = h(bl+ b2), which is half the height of the trapezoid times the sum of the two parallel bases. 

Part IV Taking the Shape of Geometric Word Problems 

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