Circle, Square, and Triangle

 

Materials and tools:

Plastic coated clothesline wire, 1 meter per student; typing paper, four sheets per student; rulers; compasses; index cards for drawing right angles; calculators (preferably TI-34 II); scissors for cutting wire; tape to join ends of the wire.

 

Task.

Cut your 1 meter wire into three parts of equal length.

WARNING: Measure twice (or three times) and cut once!

Form a circle, a square, and an equilateral triangle (precision counts!), joining the ends of the wire with tape. All three figures have the same perimeter, and this simple fact must be discussed with students who often are not sure what a perimeter is.

Using three separate sheets of paper, students should draw a circle, a square, and a triangle, congruent to those they have made from the wire, and write underneath their drawings their perimeters and their (computed) areas (rounded). The writing that is needed during the computation should be done on a separate sheet.

 

Format:

 

CIRCLE

 

 

      Perimeter = 33.3 centimeters

      Area = 88.4 square centimeters

 

 

 

SQUARE

 

      Perimeter = 33.3 centimeters

      Area = 69.4 square centimeters

 

EQUILATERAL TRIANGLE

 

      Perimeter = 33.3 centimeters

      Area = 53.5 square centimeters

 

 

Computation

 

Computation should be done with a calculator. Formulas should be given and discussed. Variables should be declared and all writing should be properly labeled on a separate sheet of paper.

 

Circle.

r       radius

A = π*r2       area

C = 2*π*r = 100/3       circumference (measured in cm)

So, r = C/(2*π) = 100/(6*π)

Program:

100/(6π)    [=]    5.30516477

πAns2    [=]    88.4194283

 

Square

s       side

A = s2       area

P = 4*s = 100/3       perimeter (measured in cm).

So, s = P/4 = 100/12

Program:

100/12    [=]    8.33333333

Ans2    [=]    69.44444444

 

Equilateral triangle.

s       side

A = √(3)/4*s2       area

P = 3*s = 100/3       perimeter (measured in cm)

So, s = P/3 = 100/9

Program:

100/9    [=]     11.11111111

√(3)/4Ans2    [=]    53.45835826

For a more detailed "Cheat Sheet" for the compuations and constructions on paper, click here.  

Here we will compare a circle, a square, and a triangle:

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