Answer 1:
My design is a geometric pattern created using a combination of squares, triangles, and hexagons. The pattern has a repeating, symmetrical design that resembles a kaleidoscope. The colors used are a mix of blues, greens, and purples to create a calming and harmonious feel.
Create an original design using only the figures given (the pages at the end of this portfolio contain shapes that can be printed). 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! Record your answers below.
Question 1
Describe your design in words. What shapes did you use? Does it have a repeating pattern? Is it abstract or does it resemble something recognizable?
9 answers
Think about the shapes you used in your design and how you will calculate the area of each one. What two strategies can you use to make it easier to find the area?
To calculate the area of each shape in the design, I can use two strategies to make it easier:
1. Break down complex shapes into simpler shapes: For example, I can break down a hexagon into triangles and then calculate the area of each triangle.
2. Group similar shapes together: Since the shapes in my design are all regular polygons with equal side lengths, I can group together shapes of the same type and calculate the area using a formula specific to that shape. This way, I can focus on calculating the area of one type of shape at a time without getting overwhelmed by the complexity of the entire design.
1. Break down complex shapes into simpler shapes: For example, I can break down a hexagon into triangles and then calculate the area of each triangle.
2. Group similar shapes together: Since the shapes in my design are all regular polygons with equal side lengths, I can group together shapes of the same type and calculate the area using a formula specific to that shape. This way, I can focus on calculating the area of one type of shape at a time without getting overwhelmed by the complexity of the entire design.
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.
Shape
Area Formula
Measurements
Area
Example: Square
A=s
s = 2 in.
A = 4 sq. in.
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.
Shape
Area Formula
Measurements
Area
Example: Square
A=s
s = 2 in.
A = 4 sq. in.
| Shape | Area Formula | Measurements | Area |
|----------|----------------------|--------------|-------------------------|
| Square | A = s^2 | s = 3 cm | A = 9 sq. cm |
| Triangle | A = 0.5 * b * h | b = 4 cm | A = 6 sq. cm (decomposed)|
| Hexagon | A = (3 * sqrt(3) / 2) * s^2| s = 2 cm | A = 6 * sqrt(3) sq. cm |
|----------|----------------------|--------------|-------------------------|
| Square | A = s^2 | s = 3 cm | A = 9 sq. cm |
| Triangle | A = 0.5 * b * h | b = 4 cm | A = 6 sq. cm (decomposed)|
| Hexagon | A = (3 * sqrt(3) / 2) * s^2| s = 2 cm | A = 6 * sqrt(3) sq. cm |
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.
shape Example: Square
area of formula: A=s ^2
meaurements: s = 2 in.
area:A = 4 sq. in.
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.
shape Example: Square
area of formula: A=s ^2
meaurements: s = 2 in.
area:A = 4 sq. in.
| Shape | Area Formula | Measurements | Area |
|----------|----------------------|--------------|-------------------------|
| Square | A = s^2 | s = 3 units | A = 9 sq. units |
| Triangle | A = 0.5 * b * h | b = 4 units, h = 3 units | A = 6 sq. units (decomposed) |
| Hexagon | A = (3 * sqrt(3) / 2) * s^2| s = 2 units | A = 6 * sqrt(3) sq. units |
|----------|----------------------|--------------|-------------------------|
| Square | A = s^2 | s = 3 units | A = 9 sq. units |
| Triangle | A = 0.5 * b * h | b = 4 units, h = 3 units | A = 6 sq. units (decomposed) |
| Hexagon | A = (3 * sqrt(3) / 2) * s^2| s = 2 units | A = 6 * sqrt(3) sq. units |
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.
Which polygon(s) did you compose a rectangle to find the area? Which polygon(s) did you decompose into simpler shapes? Which simple shapes did you use?
Describe in words how you calculated the area of each shape. Be sure to include which formulas you used.
Which polygon(s) did you compose a rectangle to find the area? Which polygon(s) did you decompose into simpler shapes? Which simple shapes did you use?
To calculate the total area of the figure I designed, I need to find the individual areas of each shape used and then add them together.
Here is how I calculated the area of each shape in the figure:
1. Square: I composed a rectangle with the square shape and used the formula A = s^2. Given that s = 3 units, the area of the square is A = 3^2 = 9 sq. units.
2. Triangle: I decomposed the triangle into two right triangles and used the formula A = 0.5 * base * height. Given that the base (b) = 4 units and the height (h) = 3 units, the area of each right triangle is A = 0.5 * 4 * 3 = 6 sq. units. Since there are two right triangles, the total area of the triangle is 2 * 6 = 12 sq. units.
3. Hexagon: For the hexagon, I used the formula A = (3 * sqrt(3) / 2) * s^2. Given that s = 2 units, the area of the hexagon is A = (3 * sqrt(3) / 2) * 2^2 = 6 * sqrt(3) sq. units.
To find the total area of the figure, I added the individual areas of each shape together:
Total Area = Area of Square + Area of Triangle + Area of Hexagon
Total Area = 9 + 12 + 6 * sqrt(3) = 21 + 6 * sqrt(3) sq. units
In summary, I composed a rectangle to find the area of the square shape, and I decomposed the triangle into two right triangles to calculate its area. The hexagon's area was calculated using its specific formula without the need to compose or decompose it further.
Here is how I calculated the area of each shape in the figure:
1. Square: I composed a rectangle with the square shape and used the formula A = s^2. Given that s = 3 units, the area of the square is A = 3^2 = 9 sq. units.
2. Triangle: I decomposed the triangle into two right triangles and used the formula A = 0.5 * base * height. Given that the base (b) = 4 units and the height (h) = 3 units, the area of each right triangle is A = 0.5 * 4 * 3 = 6 sq. units. Since there are two right triangles, the total area of the triangle is 2 * 6 = 12 sq. units.
3. Hexagon: For the hexagon, I used the formula A = (3 * sqrt(3) / 2) * s^2. Given that s = 2 units, the area of the hexagon is A = (3 * sqrt(3) / 2) * 2^2 = 6 * sqrt(3) sq. units.
To find the total area of the figure, I added the individual areas of each shape together:
Total Area = Area of Square + Area of Triangle + Area of Hexagon
Total Area = 9 + 12 + 6 * sqrt(3) = 21 + 6 * sqrt(3) sq. units
In summary, I composed a rectangle to find the area of the square shape, and I decomposed the triangle into two right triangles to calculate its area. The hexagon's area was calculated using its specific formula without the need to compose or decompose it further.
11 answers