We will use a TI-34II calculator for the computations. A compass, ruler, and index card are also needed for drawing the figures.
1. Circle
perimeter = circumference = 33 1/3 cm
circumference = 2*
*radius
≈ 3.14159...
C = 2r. We want to
draw our circle. We know C and we want
r.
33 1/3 = 2r. Solving for r,
(33 1/3)/(2)
= (2r)/(2) = r
So r = (33 1/3)/(2)
Using a TI-34 calculator:
[2nd][FracMode][ENTER]
[33][UNIT][1][/][[3] / is the “fraction” divide
[¸][(][2][][)][ENTER] 
is the “regular” divide
display: 5.30516477
So the radius of our circle is about 5.3 cm.
To draw the circle:
Set compass at 5.3 cm and draw a circle.
What is the circle’s area?
Area of a circle = *r2
We still have r on the calculator’s display. So get r2, press
[x2][*][][ENTER]
display: 88.41941283
So the area of the circle is about 88.4 square centimeters.
We can begin to fill out a chart:
|
figure |
perimeter |
area |
|
circle |
33 1/3 cm |
88.4 sq cm |
|
square |
33 1/3 cm |
|
|
equilateral triangle |
33 1/3 cm |
|
2. Square
perimeter = 33 1/3 cm
What is the length of one side? ¼ of the perimeter:
[33][UNIT][1][/[3]
[][4][ENTER][êD][ENTER]
display: 8.33333...
So the length of one side of the square is about 8.3 cm.
To draw the square:
a. Draw a segment of length 8.3 cm.
b. Mark 8.3 cm on two adjacent sides of an index card. Use the card to make right angles from your segment.
c. Complete your square.
What is the area of the square?
Area of a square = length*width
Here, length = width = 8.3333... cm
[x2][ENTER]
display: 69.44444444
So the area of the square is about 69.4 square centimeters. We add this to our chart:
|
figure |
perimeter |
area |
|
circle |
33 1/3 cm |
88.4 sq cm |
|
square |
33 1/3 cm |
69.4 sq cm |
|
equilateral triangle |
33 1/3 cm |
|
How does the square’s area compare to the circle’s area?
3. Equilateral triangle
perimeter = 33 1/3 cm
What is the length of one side? 1/3 of the perimeter
[33][UNIT][1][/[3]
[][3][ENTER][êD][ENTER]
display: 11.1111..
So the side length of the triangle is about 11.1 cm
To draw the triangle:
a. Draw a segment with length 11.1 cm. Its two ends are two vertices of the triangle.
b. Open your compass to an 11.1 cm radius.
c. Place the compass point on one end of the segment and swing an arc.
d. Place the compass point on the other end of the segment and swing another arc that intersects with the first one. This intersection point is the third vertex of your triangle.
e. Finish drawing your triangle.
What is the area of the triangle?
Area of triangle = ½ *base*height = ½ bh. And b = 1.1 cm
One way to find the height:
Use an index card to draw the height. Slide the card along the base until it meets the vertex. Draw the height. Now measure it with a ruler. It will be about 9.6 cm.
The length of the base is still on the calculator’s display. To compute the area:
[*][9.6][][2][ENTER]
display: 53.3333...
So the area of the triangle is about 53.3 sq cm.
We can now finish our chart:
|
figure |
perimeter |
area |
|
circle |
33 1/3 cm |
88.4 sq cm |
|
square |
33 1/3 cm |
69.4 sq cm |
|
equilateral triangle |
33 1/3 cm |
53.3 sq cm |
Compare the triangle’s area with the areas of the circle and the square.
Punch line:
Figures with the same perimeter do not necessarily have the same area.
(And for a given perimeter, the circle has the biggest
area.)
Last Modified: January 16, 2006