Name _______________________________
Date _________________
Using a Graph to Find Area
Introduction: In this activity, you will be using a sample of ordinary poster board with uniform thickness to
study area. Since the thickness is constant, you can measure the mass and area of rectangular poster board
samples and graph the data to find a relationship between mass and area (mass/area). Using the graph, you will
then be able to find the unknown area of an irregularly shaped sample of poster board.
Purpose:
1. To calculate and graph the area of four regularly shaped samples of poster board.
2. To use the graph to find the area of an irregularly shaped sample of poster board.
Materials: Balance
4 samples of poster board of regular shape
graph paper
pencil
1 irregular sample
ruler
Procedure:
1. Obtain four rectangles of poster board from the teacher. Notice that each piece has been labeled with a
letter or number. Please record this letter or number in your data table.
2. Find the mass of each sample of poster board and record the mass of each in the data table.
3. Measure the length and width of each sample to the nearest .1 cm. Record these measurements under length
and width in the data table.
4. Calculate the area of each sample of poster board.
5. Obtain an irregular piece of poster. Find the mass and record the mass in the data table.
Data Tables:
Rectangle Code
Mass
Irregular Sample
Length
Width
Mass
* Note: The Area will be determined after you construct the graph below.
Area
Area*
6. Plot a graph of mass versus area for your rectangular samples. Place mass on the x-axis and area on the yaxis. Be sure to label each axis.
7. Locate the mass of your irregular object on the line of your graph and determine its area by moving across
horizontally to the y-axis. Record the area in the data table. Show this interpolation on your graph.
Conclusions:
1. What is interpolation?
2. Use your graph to find the mass of a poster board sample with an area of 300 cm2. Be sure to draw this on
your graph as well as write the answer here.
3. What is the area of a sample of poster board that has a mass of 8.5 grams? Be sure to draw this on your
graph as well as write the answer here.
4. Find the area of a sample that has a mass of 25 grams. Be sure to draw this on your graph as well as write
the answer here.
5. Find the mass of a sheet of poster board measuring 7.12 cm by 56.4 cm. Be sure to draw this on your graph
as well as write the answer here.
Using a Graph to Find Area
Student Data Pages - Answers
Numerical data in the data table will depend on the pieces of poster board used. It does not matter what sized
pieces are used. Cut the poster board into 4 pieces of regular size. Make each piece a different size. Make sure
that the pieces will fit on a balance.
Conclusions:
1.
What is interpolation? Using the data on the graph to answer a new and different question; inferring the
answer to a new question based on the data obtained in the lab.
2.
Use your graph to find the mass of a poster board sample with an area of 300 cm2. Be sure to draw this on
your graph as well as write the answer.
On the y axis of the graph, find 300 cm2. Draw a line from this point until it intercepts the line on the
graph. At the interception point, draw a line downward until it reaches the x axis. The point where it hits
the x axis is the answer to the question.
3.
What is the area of a sample of poster board that has a mass of 8.5 grams? Be sure to draw this on your
graph as well as write the answer.
On the x axis of the graph, find 8.5 g. . Draw a line from this point until it intercepts the line on the graph.
At the interception point, draw a line to the left until it reaches the y axis. The point where it hits the y axis
is the answer to the question.
4.
Find the area of a sample that has a mass of 25 grams. Be sure to draw this on your graph as well as write
the answer.
On the x axis of the graph, find 8.5 g. . Draw a line from this point until it intercepts the line on the graph.
At the interception point, draw a line to the left until it reaches the y axis. The point where it hits the y axis
is the answer to the question.
5.
Find the mass of a sheet of poster board measuring 7.12 cm by 56.4 cm. Be sure to draw this on your
graph as well as write the answer.
Area = 7.12 cm x 56.4 cm = 401.568 cm2
On the y axis of the graph, find 401.568 cm2. Draw a line from this point until it intercepts the line on the
graph. At the interception point, draw a line downward until it reaches the x axis. The point where it hits
the x axis is the answer to the question.
Teacher Preparation Notes:
1.
Numerical data in the data table will depend on the pieces of poster board used. It does not matter what
sized pieces are used. Cut the poster board into 4 pieces of regular size. Make each piece a different size.
Make sure that the pieces will fit on a balance.
2.
Cut one piece of poster board into an oddly shaped irregular size. Once the graph has been constructed
using the data from the 4 regularly shaped pieces, you will use interpolation to find the area of the irregular
piece.
3.
It is helpful to write numbers or letters on each piece of poster board and have the students record these
numbers or letters in their data. It will make grading easier for you.