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!
One possible design could be a field of tulips, with the triangles forming the petals and the squares forming the leaves. The triangles can be arranged in a circular pattern to create the shape of a tulip, with the squares placed below to represent the leaves. Using different colors for the shapes can enhance the effect and give the design a more realistic look. This design takes advantage of the geometric nature of the shapes to create a visually appealing and creative image.
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?
To calculate the area of the shapes used in the tulip design, we will need to measure the side lengths of the triangles and squares and then apply the appropriate formulas.
Here is a table showing the measurements for each shape:
Shape Side Length
Triangle 2 cm
Square 2 cm
To find the area of the triangle, we will use the formula:
Area = (base x height) / 2
Area = (2 cm x 2 cm) / 2
Area = 2 cm²
To find the area of the square, we will use:
Area = side x side
Area = 2 cm x 2 cm
Area = 4 cm²
Now, to calculate the total area of the tulip design, we can decompose it into simpler shapes. We can see that the tulip shape consists of 4 triangles and 1 square.
Total area = (Area of 4 triangles) + (Area of 1 square)
Total area = (4 x 2 cm²) + 4 cm²
Total area = 8 cm² + 4 cm²
Total area = 12 cm²
Therefore, the total area of the tulip design is 12 cm².
I found the area of each shape by using the basic area formulas for triangles and squares. To find the total area, I decomposed the tulip shape into individual triangles and a square, and then added up their areas to get the total area of the design.
To create the shapes, use a ruler and draw each shape on a piece of paper. The side lengths for each shape should be the same. For example, if the equilateral triangle has three-inch sides, then three inches must be used for the sides on all other shapes.
The only exception is the long side of the trapezoid. The long side will be twice the unit size of the top and sides. For example, if you make each side length three inches, the longer side of the trapezoid will measure six inches.
Equilateral triangle
60°
rhombus
Trapezoid
Regular hexagon
Square Or Make a description
Instructions for creating the shapes:
1. Equilateral Triangle:
Draw a triangle with all three sides measuring the same length (e.g. 3 inches). Each angle should be 60 degrees.
2. Rhombus:
Draw a rhombus with all four sides measuring the same length as the sides of the equilateral triangle (e.g. 3 inches). Make sure that the opposite angles of the rhombus are equal.
3. Trapezoid:
Sketch a trapezoid with the top and side lengths measuring the same as the equilateral triangle (e.g. 3 inches). The longer base of the trapezoid should be twice the length of the other sides (e.g. 6 inches).
4. Regular Hexagon:
Create a hexagon with all six sides measuring the same length as the equilateral triangle (e.g. 3 inches). Each interior angle should be 120 degrees.
5. Square:
Draw a square with all four sides measuring the same as the equilateral triangle (e.g. 3 inches).
By following these instructions and using the specified side lengths, you can create all the required shapes for the design.