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?
I used the formulas for finding the area of a square (side length squared), triangle (base times height divided by 2), and rectangle (length times width).
To find the area of each shape, I first measured the side length of the square and used that measurement to calculate the area. For the triangle, I measured the base and height and plugged those measurements into the formula to find the area. For the rectangle, I measured the length and width and used those measurements to calculate the area.
For one of the shapes, I composed a rectangle by placing two squares together to create a larger square, then found the area of that new rectangle using the formula length times width. For another shape, I decomposed it into simpler polygons (like squares and triangles) and found the area of each of those shapes separately before adding them all together to find the total area of the shape I designed.
By using these methods, I was able to accurately calculate the area of each shape and then find the total area of my entire design.
give me an example for all of them
Sure! Here is an example of each step using a design with a square and a triangle:
1. Design:
I created a design using a square and a triangle placed together in a pattern on the paper.
2. Measurements:
- The square has a side length of 4 inches.
- The triangle has a base of 4 inches and a height of 3 inches.
3. Calculations:
- Area of the square: Side length squared = 4 inches * 4 inches = 16 square inches.
- Area of the triangle: Base times height divided by 2 = 4 inches * 3 inches / 2 = 6 square inches.
4. Total Area:
To find the total area of the design, I compose a rectangle using the square and triangle:
- The rectangle would have a length of the side length of the square (4 inches) and a width of the height of the triangle (3 inches).
- Area of the rectangle: Length times width = 4 inches * 3 inches = 12 square inches.
5. Description:
For the square, I used the formula for the area of a square. For the triangle, I used the formula for the area of a triangle. To find the total area, I composed a rectangle by placing the square and triangle together and calculated the area of the resulting rectangle.