Which of the following is NOT a method of determining the area of a geometric shape?

Measuring the perimeter does not provide a method for determining the area of a geometric shape. The perimeter refers to the total distance around the boundary of a shape, which is a one-dimensional measure. In contrast, area is a two-dimensional measure that quantifies the space contained within the boundaries of a shape.

The other options represent valid methods for calculating area. Standard formulas are often established for common geometric shapes; for example, the area of a rectangle is determined using the formula length multiplied by width. Counting square units involves physically dividing a shape into smaller squares (or using grid overlays) to find how many squares fit within its boundaries. Additionally, integral calculus provides a method for finding area, particularly for irregular shapes, by breaking them down into infinitely small pieces and summing them up. Thus, while perimeter is related to dimensional analysis, it does not apply to area calculations.