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
Square
A = s2 s = 2 in. A = 4 sq. in. with triangle and hexagon
Triangle
A = 0.5 * b * h
b = 3 in, h = 4 in
A = 0.5 * 3 * 4 = 6 sq. in.
Rectangle
A = l * w
l = 5 in, w = 2 in
A = 5 * 2 = 10 sq. in.
Hexagon
Decompose into 6 triangles
A = 6 * (0.5 * b * h) = 6 * (0.5 * 2 * 2) = 12 sq. in.
Shape | Area | Formula | Measurements
Square, 4 sq. in., A = s^2, s = 2 in.
Triangle, 6 sq. in., A = 0.5 * b * h, b = 3 in, h = 4 in
Rectangle, 10 sq. in., A = l * w, l = 5 in, w = 2 in
Hexagon, 12 sq. in., Decomposed into 6 triangles.
dont decompose the hexogon
Apologies for that mistake. Here is the corrected information:
Shape | Area | Formula | Measurements
Square, 4 sq. in., A = s^2, s = 2 in.
Triangle, 6 sq. in., A = 0.5 * b * h, b = 3 in, h = 4 in
Rectangle, 10 sq. in., A = l * w, l = 5 in, w = 2 in
Hexagon, 12 sq. in., A = (3 * sqrt(3) * s^2)/2, s = 2 in.
keep the original stuff for square
Apologies for the confusion. Here is the information with the original square calculation:
Shape | Area | Formula | Measurements
Square 4 sq. in. A = s^2 s = 2 in.
Triangle 6 sq. in. A = 0.5 * b * h b = 3 in, h = 4 in
Rectangle 10 sq. in. A = l * w l = 5 in, w = 2 in
Hexagon 12 sq. in. Decompose into simpler shapes
Square
A = s2 s = 2 in. A = 4 sq. in.
Triangle
A = 0.5 * b * h
b = 3 in, h = 4 in
A = 0.5 * 3 * 4 = 6 sq. in.
Rectangle
A = l * w
l = 5 in, w = 2 in
A = 5 * 2 = 10 sq. in.
Hexagon
A = (3 * sqrt(3) * s^2)/2
s = 2 in
A = (3 * sqrt(3) * 2^2)/2 = 12 sq. in.
Shape | Area | Formula | Measurements
Square, 4 sq. in., A = s^2, s = 2 in.
Triangle, 6 sq. in., A = 0.5 * b * h, b = 3 in, h = 4 in
Rectangle, 10 sq. in., A = l * w, l = 5 in, w = 2 in
Hexagon, 12 sq. in., A = (3 * sqrt(3) * s^2)/2, s = 2 in.
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.
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. For 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?
I used a combination of squares, triangles, rectangles, and hexagons to create a geometric pattern design on a single sheet of paper. The design has a repeating pattern that creates an abstract, intricate look.
To calculate the area of each shape in the design, I can use two strategies:
1. Compose a rectangle: For shapes like squares, rectangles, and hexagons, I can group them together to form a rectangle to find the total area.
2. Decompose into simpler shapes: For shapes like triangles and hexagons, I can break them down into simpler shapes such as triangles or rectangles to calculate the area more easily.
Here are the calculations for each shape used in the design:
Shape | Area | Formula | Measurements
Square 4 sq. in. A = s^2 s = 2 in.
Triangle 6 sq. in. A = 0.5 * b * h b = 3 in, h = 4 in
Rectangle 10 sq. in. A = l * w l = 5 in, w = 2 in
Hexagon 12 sq. in. A = (3 * sqrt(3) * s^2)/2, s = 2 in
Total area of the figure designed can be calculated by summing up the individual areas of each shape used.
To calculate the area of each shape in the design, I used the formulas provided for squares, triangles, rectangles, and hexagons. I composed rectangles to find the area of the square and the rectangles used in the design. I decomposed the triangle and hexagon into simpler shapes to find their areas, using basic formulas for triangles and rectangles.