Finding Area by Decomposing & Rearranging

———————————————————————————————————————————————————

Find Area of a Regular Plane Figure by Counting Enclosed Squares.

  • Check the Hint box if you need help.​

A.

B.

C.

D.

E.

F.

G.

———————————————————————————————————————————————————

Finding Area by Decomposing and Rearranging.

Use the applet below to investigate the relationship between the formula for the area of a rectangle and the formula for the area of a parallelogram.

  • Pull the slider to the right to create a new figure.​

———————————————————————————————————————————————————

Creating complex shapes From Simple Regular Polygons.

(A). This app has one square and some small, medium, and large right triangles. Click on a shape and drag to move it. Grab the point at the vertex and drag to turn it.The area of the square is 1 square unit.

(1). Write a definition of area that includes all the information that you think is important: 

(2). Use these shapes to create a new shape with an area of 1 square unit that is not a square.

(3). Notice that you can put together two small triangles to make a square. What is the area of the square composed of two small triangles?

(4). Use your shapes to create a new shape with an area of 2 square units.

(5). Use your shapes to create a new shape with an area of 4 square units.

(6). Use your shapes to create a DIFFERENT SHAPE with an area of 2 square units.

(7). Find a way to use all of your pieces to compose a single large square.

(8). What is the area of the large square you created in the app above?

(9). The area of the small triangle is ____________ square units.

(10). The area of the medium triangle is ____________ square units.

(11). The area of the large triangle is ____________ square units.

———————————————————————————————————————————————————

Priya decomposed a square into 16 smaller, equal-size squares and then cut out 4 of the small squares and attached them around the outside of original square to make a new figure as shown below.

———————————————————————————————————————————————————

This rectangle has been decomposed along its diagonal. Recompose the two pieces to make a different shape.

How does the area of this new shape compare to the area of the original rectangle? Explain how you know.

———————————————————————————————————————————————————