Exploring a Dot Grid Through Rectangles

You have calculated areas and perimeters of figures like rectangles, triangles, maybe even circles many times. Have you ever wondered what the relationship between area and perimeter of a figure is? What happens when area increases? Does the perimeter increase or decrease? What happens to the area if the perimeter decreases? Here we will explore the relationship between area and perimeter of rectangles. We will do this however with an important constraint – the rectangles will be those that can be drawn on a dot grid such that the corners (vertices) of the rectangles are grid points.