Lab
Lab: Triangle Measurements
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In this measurement lab, you will be using a meter stick (or 30-cm ruler) to measure the base and height of your triangle(s). You will also be using a triple beam balance to measure the mass of each triangle. Before starting, each team needs a #2 pencil, a pair of scissors, a meter stick (0r 30 cm ruler), a protractor, a triple beam balance, and access to the Internet to submit your data and conclusions. In the second part of the lab you will need to use EXCEL and print your graphs.
Part I: Measurements
Before using your scissors to reduce the size of your triangle, measure its initial base, height, and hypotenuse. Measure each to the nearest 1/10
^{th}
of a centimeter.
base (in cm) equals
height (in cm) equals
hypotenuse (in cm) equals
Using the Pythagorean Theorem, verify that your triangle is a right triangle.
yes, it is
no, it is not - call your instructor to your lab station if this choice is necessary
Using a protractor (or your knowledge of 45-45-90 right triangles), verify that the two acute angles of your triangle are 45º.
Next, use a triple beam balance to measure the gravitational mass of your triangle to the nearest 1/100
^{th}
of a gram. Remember that your balance must be zeroed before any measurements can be taken.
mass (in grams) equals
Now we will begin reducing the size of our triangle by measuring and cutting off 5-cm "layers" from the base.
You should be able to measure at least 6 smaller triangles - if possible, continue until you have no more than 10. Be very careful to keep your "cutting lines" at right angles to the height of the triangle. Do not cut slanted lines.
trial
base
height
mass
(cm)
(cm)
(grams)
1
2
3
4
5
6
7
8
9
10
Recall from geometry that the area of a triangle equals ½bh. Now you need to calculate the area of all triangles (including the original).
triangle
area
mass
trial
(cm
^{2}
)
(grams)
original
1
2
3
4
5
6
7
8
9
10
Part II: Data Analysis
Using a school laptop, open the EXCEL file called
trianglemeasures.xlsx
on the E:// drive. There is a short cut on each laptop's desktop.
Fill in the names of your group members and your group's area and mass data. Save the file as trianglemeasures_LastnameLastname.xlsx
As you fill in the data table, a line should "grow" in the chart area.
When your graph is finished, print out one copy for Mrs. Colwell. If you also want copies, you may print a copy for each lab member to place in your notebook.
Resave your file and close EXCEL.
What is the name of your EXCEL file?
What was the slope of your line?
What was the y-intercept of your line?
What was the correlation coefficient (R
^{2}
) of your line?
Using unit analysis and your knowledge from Algebra I, what are the units on the slope of your line?
Part III. Conclusions and Extensions
You will now be given an irregular shape cut from the same cardboard as your triangle. Measure its mass. Then using the equation of your line (y = mx + b) displayed by EXCEL on your graph, interpolate the area of your irregular shape.
mass (in graphs) of irregular shape
area (in cm
^{2}
) of your irregular shape based on the equation of your EXCEL graph
Now, using a ruler or meter stick, divide your irregular shape into combinations of triangles and rectangles. Using a protractor to determine the positions of altitudes for each triangle, measure the length of the base and height of each triangle. Labels these dimensions (in #2 pencil) on your irregular shape. If any rectangles are present, also measure their lengths and widths and label those dimensions (in #2 pencil) on the irregular shape.
Finally calculate the area of each of the constituent triangles and rectangles. Place those values in the center of each one.
What is the total area (in cm
^{2}
) of your irregular shape?
What is your group's percent difference between the two area values: one obtained from the equation, the other from the actual area calculations?
Explain why the two area values should have been identical.
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