Illuminations: Shape Cutter

# Shape Cutter

With this tool, you can explore how to decompose shapes and recompose them to make other shapes. You can draw and cut shapes and also use slides, turns, and flips to move pieces around.

### Instructions

 Draw points on the grid. As each point is drawn, it will be connected to the previous point. When you want to complete a polygon, click on the first point again; the last point will be connected to the first point, and the polygon will be colored. After the polygon is drawn, click two points along the perimeter of the polygon. These points will be connected to form a "cut line." Place other pairs of points along the perimeter to form other cut lines. When all cut lines are placed, press the Cut button to cut the polygon into pieces. The divided pieces can be moved, or you can Slide, Flip, or Turn them with the appropriate button. The Mix Up button will move the pieces around. Selecting "Don't Flip" will prevent the pieces from being reflected when they are mixed. The New Shape button resets the drawing area.

### Exploration

 Create a polygon with at least five sides. Then, place at least three cut lines across the figure. (Be sure that some of the cut lines overlap.) Mix the pieces up with the Mix Up button. Can you rearrange the pieces back to their original shape? For a slightly more advanced exploration, try this: Create a parallelogram. Draw a cut line from one vertex that is perpendicular to the opposite side, then hit the Cut button. Rearrange the pieces to form a rectangle. The area formula for a rectangle is A = bh. The area formula for a parallelogram is also A = bh. How does this rearrangement help you understand why the same formula is used for these two different shapes? Cut a rectangle into three pieces as follows: Choose two adjacent vertices, and draw a cut line from each vertex to the same point on the opposite side. Rearrange the two smaller pieces so that they cover the larger piece. How does this help you understand how the formula for finding the area of a triangle is related to the formula for finding the area of a rectangle?

 We're sorry, but your browser does not seem to be fully capable of running this activity. You must be using either Internet Explorer 4 or later, or Netscape Navigator 4 or later, to view this activity. If you are using one of these browsers, it is likely that you do not have JavaScript enabled. Please enable it under Options/Preferences in your browser's menu.

### Lessons

 More and Better Mathematics for All Students
 © 2000 National Council of Teachers of Mathematics Use of this Web site constitutes acceptance of the Terms of Use The National Council of Teachers of Mathematics is a public voice of mathematics education, providing vision, leadership, and professional development to support teachers in ensuring mathematics learning of the highest quality for all students. The views expressed or implied, unless otherwise noted, should not be interpreted as official positions of the Council.