Question

Use Area to Solve Problems Portfolio

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.

Answer 1

[AI-generated answer — Bot GPT 3.5]

Design Description:

For my original design, I decided to create a geometric pattern using a combination of squares, triangles, and hexagons. The design features a repeating pattern that forms a visually appealing and intricate shape. By arranging the shapes in different ways, I was able to create a unique and eye-catching design that fits seamlessly together.

Shapes Used:
- Square
- Triangle
- Hexagon

Design Result:
The final design is a tessellating pattern that showcases the different shapes coming together to form a cohesive and harmonious whole. The use of straight lines and angles gives the design a clean and modern look, while the repetition of shapes adds a sense of symmetry and balance. Overall, I am pleased with how the design turned out and enjoyed the creative process of using area to solve problems in a visual way.

Answer 2

make it shorter and make it sound different

Answer 3

[AI-generated answer — Bot GPT 3.5]

Design Description:

My design is a modern and visually appealing pattern created using a combination of squares, triangles, and hexagons. By arranging the shapes in a repeating pattern, I was able to achieve a balanced and harmonious design that showcases the unique qualities of each shape. The use of straight lines and angles gives the design a clean and geometric look, while the repetition of shapes adds an interesting visual element.

Shapes Used:
- Square
- Triangle
- Hexagon

Design Result:
The final design is a tessellating pattern that highlights the versatility of the shapes used. The design is cohesive, intricate, and eye-catching, making for an engaging visual experience. Overall, I enjoyed the creative process of using area to solve problems in a unique and artistic way.

Answer 4

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?

Answer 5

[AI-generated answer — Bot GPT 3.5]

When calculating the area of the shapes used in my design (square, triangle, hexagon), there are two strategies that can make it easier to find the area:

1. Break down complex shapes into simpler shapes: For example, if I have a hexagon in my design, I can break it down into triangles and/or rectangles to calculate the area more easily. By decomposing complex shapes into simpler ones, it becomes simpler to find the total area.

2. Use formulas: Each shape has a specific formula for calculating its area. By using the formulas for squares, triangles, and hexagons, I can quickly and accurately determine the area of each shape in my design. This approach is a straightforward and efficient way to calculate the total area of the design.

By applying these strategies, I can effectively calculate the area of each shape in my design and determine the total area covered by the tessellating pattern.

Answer 6

MAKE IT WAY SHORTER

Answer 7

[AI-generated answer — Bot GPT 3.5]

To make finding the area of the shapes in my design easier, I can break down complex shapes into simpler ones and use the specific formulas for squares, triangles, and hexagons.

Answer 8

ITS ONE SHAPE USING THE SHAPE YOU SAID TO MAKE A DIFFERENT ONE

Answer 9

[AI-generated answer — Bot GPT 3.5]

To calculate the area of the hexagon in my design, I can break it down into equilateral triangles and use the formula A = (1/2)bh or the formula for a regular hexagon, A = (3√3/2)s^2, where s is the length of a side.

Answer 10

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.

Answer 11

[AI-generated answer — Bot GPT 3.5]

I'm sorry, but as a text-based AI, I am unable to physically interact with a ruler or measure anything. However, I can guide you on how to measure and calculate the area of shapes using a ruler and the appropriate formulas.

Here is a sample table to record your measurements and calculations:

| Shape | Measurements | Formula Used | Calculation |
|----------|------------------|-----------------|-------------------------------|
| Square | Side Length = s | A = s^2 | A = (side length)^2 |
| Triangle | Base = b, Height = h | A = (1/2)bh | A = (1/2)(base)(height) |
| Hexagon | Side Length = s | A = (3√3/2)s^2 | Calculate using formula |

Remember to measure the appropriate sides for each shape and then use the corresponding formula to calculate the area. Use the given formulas to perform the calculations and fill in the table accordingly. Let me know if you need any further assistance.