Seeing Circles

Open the PDF called Circles and Triangles.  Here is the link to find the actual problem.

Link for Circles and Triangles

This POW may take two periods.  Answer all the questions.  You will need to use paint for this activity.  If you need help let me know.  You can put your answers in a word document (make sure to cut and paste your illustrations in the document,) and e-mail to outr math class honors email and entitle it "Seeing Circles."  Make sure you name is somewhere in the document.  (Not on the picture please.)  I will post your responses on our webpage.  I will include the link here when they are uploaded.

Some things I noticed.  Many of your comments or solutions are numbered and there is no hint of the what the question was you were trying to answer.  Be sure that you follow the 6-traits and embed the question in your response. Your illustrations of your thinking were wonderful, and most of you were spot on with your solutions.

To see your solutions you can go to our website or click on the link below:

YOUR SOLUTIONS

1. To achieve the maximum area, the triangle must have the maximum height. This maximum height is 8 units. The area of triangle ABC is  ½ • (16 units) • (8 units) = 64 sq. units.

2. An area that is half of the maximum area can be achieved by choosing a height that is half of the maximum height, which is a height of 4 units.

There are four possible points C. One of the four possibilities is pictured. For any of the four possible triangles, the area is ½ • (16 units) • (4 units) = 32 sq. units.

3. The area can be made smaller by decreasing the height. If we place C very close to A, the area of the triangle can be made as small as desired. If C actually coincides with A, the area becomes 0, but ABC is arguably no longer a triangle.