Use Area to Solve Problems Portfolio

Question

Worksheet
Directions: Use this worksheet to record your answers to the activity. When you
are finished, save this worksheet with your answers and submit it for a portfolio
grade.
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.
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?
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?
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 = s2 s = 2 in. A = 4 sq. in

Answer 1

Design description: My design uses a combination of squares, triangles, and hexagons. It has a repeating pattern that forms a geometric shape resembling a flower.

Two strategies to make it easier to find the area:
1. Composing a rectangle: Use multiple shapes to form a rectangle and then find the area of the rectangle.
2. Decomposing into simpler shapes: Break down a shape into simpler shapes (e.g., triangles, rectangles) and find the area of each simpler shape.

Table of measurements and area calculations:
Shape | Area Formula | Measurements | Area
Square | A = s^2 | s = 3 in. | A = 9 sq. in.
Triangle | A = (1/2) * b * h | b = 4 in., h = 2 in. | A = 4 sq. in.
Hexagon | A = (3sqrt(3) * s^2) / 2 | s = 2 in. | A = 6sqrt(3) sq. in.