Activity 12R (Perimeter Misconceptions)

Johnny's method for calculating the perimeter of the shaded shape in the figure at the left is to shade the squares along the border of the shape, as shown in the figure on the right. Johnny counts these border squares and says the perimeter of the shape is 26 units. Is Johnny's method valid? Why or why not? I have included the Text, Segment, and Point tools if they help you to label the figure(s) in your explanation.

Using the distance tool, measure the length of the diagonal line segment in the shaded shape. Then explain why the shape does not have a perimeter of 15 cm. Distance Tool: Click the distance tool and then the object you wish to measure (in this case, the diagonal line segment).

Draw a shape that has a perimeter 15 cm on the same graph paper. The corners of your shape do not have to be located where grid lines meet. Explain how you figured out how to make your shape.