give me an example for all of them
1. 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!
2.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?
3.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.
4.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.
5.Calculate the total area of the figure you designed. Show your work. Include the correct units for area in your answer.
4.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?
1. For my design, I used a combination of squares, triangles, and hexagons. I created a pattern where the triangles and squares alternated around the hexagon. It ended up looking like a flower shape.
2. To make it easier to find the area of each shape, I used the fact that all the shapes had equal side lengths. This allowed me to use simpler formulas for each shape.
3. I used a ruler to measure the side lengths of each shape. For the squares, I only needed to measure one side length since they were all the same. For the triangles, I measured the base and height. And for the hexagons, I measured the apothem and the side length.
4. To calculate the area of each shape, I found the area of the squares by simply squaring the side length. For the triangles, I used the formula Area = 1/2 * base * height. And for the hexagons, I used the formula Area = 3/2 * apothem * side length.
5. The total area of my design was the sum of the areas of all the shapes. I calculated it by adding up the areas of the squares, triangles, and hexagons. The total area was 75 square inches.
6. I calculated the area of each shape by using the appropriate formulas. For the squares, I used the formula Area = side length * side length. For the triangles, I used the formula Area = 1/2 * base * height. And for the hexagons, I used the formula Area = 3/2 * apothem * side length. I composed a rectangle to find the area of some shapes and decomposed others into simpler polygons.