For this activity you will need an 8 ½ x 11 inch sheet of paper, a pencil, and a ruler.
Create an original design using only the figures given. The side lengths of all of the shapes are the same so that you can line up their edges to create a tiling. Your design can use any combination of shapes, but you must use at least one of each shape in your design. The design you create can be as simple or as complex as you want. It can have a repeating pattern or it can be random, but it must fit on a single sheet of paper. Your design can make a recognizable shape or it can be abstract. Use your imagination!
Think about the shapes you used in your design and how you will calculate the area of each. Are there any ways you can make it easier to find the area?
Use a ruler to make any measurements you need to find the area of each shape. Refer to your formulas to find out which measurements you will need. Record your measurements in a table.
Calculate the area of each shape you used. Find the area of at least one shape by composing a rectangle. Find the area of at least one shape by decomposing it into simpler shapes. Record your calculations in a table.
Calculate the total area of the figure you designed. Show your work. Include the correct units for area in your answer.
Describe in words how you calculated the area of each shape. Be sure to include which formulas you used. Did you compose a rectangle to find the area or did you decompose the shape into simpler polygons?
For example, if your design includes squares and triangles, you can use the formula A = s^2 for the squares, where s is the length of a side, and the formula A = 0.5bh for the triangles, where b is the base and h is the height. To find the area of the squares, you will simply square the length of one side. To find the area of the triangles, you may need to decompose them into right triangles first, then use the formula for the area of a triangle.
To calculate the total area of the figure, add up the areas of all the shapes you used in your design. Make sure to include the correct units in your final answer – square inches in this case.
When describing how you calculated the area of each shape, be sure to explain which formula you used and how you applied it. Did you decompose any shapes into simpler polygons in order to find the area more easily? Be specific in your explanation.