Unit 1: Collection, Display, And Interpretation Of Data Worksheet - 6th Grade Page 34
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44Date
Time
LESSON
Using a Graph to Find the Largest Area
1 10
Math Message
212,
214, 215
Suppose you have enough material for 22 feet of fence. You want to enclose the
largest possible rectangular region with this fence.
If you know the perimeter and length of a rectangle, how can you find its width?
1.
The table below lists the lengths of some rectangles with a perimeter of 22 feet. Fill
2.
in the missing widths and areas. You may want to draw the rectangles on your grid
paper. Let the side of each grid square represent 1 foot.
Length (ft)
1
2
3
4
5
6
7
8
9
10
Width (ft)
10
9
Perimeter (ft)
22
22
22
22
22
22
22
22
22
22
2
Area (ft
)
28
10
18
If you have not already done so, draw each rectangle from the table above on
3.
your grid paper.
What are the length and width of the
4. a.
rectangle(s) in the table with the largest area?
ft
ft
2
What is that area?
ft
b.
On the graph on page 35, plot the length and area of each rectangle in the table.
5.
Do not connect the plotted points yet.
Find a rectangle whose perimeter is 22 feet and whose area is larger than
6. a.
the area of the rectangle in Problem 4 above. Use your graph to help you.
2
What is the length?
ft Width?
ft Area?
ft
Now plot the length and area of this rectangle on the grid on page 35.
b.
Then draw a curved line through all the plotted points.
34
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