4.8c Building Squares
Holt Course 3
Name: ______________________________
Previously, you had some squares that were “upright” and some that were “tilted”. The upright
squares were easy to work with and their side lengths were easy to compute. However, the titled
squares took a bit more work when finding their areas. And, when finding their side lengths, the
tilted squares did not have integer answers. Instead their side lengths were left in radical form.
For instance…
The square below has an area of 4 un2.
Therefore, its side length is
4un 2 = 2 un.
The square below has an area of 2 un2.
Therefore, its side length is 2un 2 = 2un .
You can use the facts of square roots and areas of squares to find the length of a line segment drawn
on dot paper. For example, to find the length of the line segment drawn below (figure #1), you first
need to draw a square that has a side length equal to the original segment length (figure #2). Then,
you need to find the area of the square (figure #3). Finally, you need to find the square root of the
area to find the original line segment’s length (figure #4)
The area of the square is
5 un2. Therefore the side
length of the square is
5un 2 = 5un
After understanding the above topics, here is your job. On the dot paper on the third page are
line segments of varying lengths. For each line segment, do the following:
1) Make a square out of each line segment. Each square you make needs to have a side length
that is equal to the segment given. No square should overlap with another square.
2) Once you carefully have drawn your square, check with your group members to confirm that
your squares are correct. There is only one-way to draw all of the squares without any
overlapping. If needed, respectfully resolve any differences.
3) Find the area of each square and record your answer in the table on the back of this page.
Remember your correct labels on your answers.
4) Finally, using what you know about square roots find the length of each of the original line
segments. Remember your correct labels on your answers and round to the nearest 100th
Adapted from Lappon, Fey et al. Looking For Pythagoras. (Connected Mathematics), Dale
Seymour Publications © 1998
Reminder: The distance between two points horizontally or vertically is equal to one unit (1 un).
Therefore, the area of a square with side lengths equal to one unit (1 un) is one square unit (1 un2).
Remember that going diagonally from one dot to another is NOT equal to one unit (1 un).
Line
Segment
Area of
Square
Length of
Line Segment
Line
Segment
AB
AI
AC
AJ
AD
AK
AE
AL
AF
AM
AG
AN
AH
AO
Area of
Square
Length of
Line Segment
Adapted from Lappon, Fey et al. Looking For Pythagoras. (Connected Mathematics), Dale
Seymour Publications © 1998
Adapted from Lappon, Fey et al. Looking For Pythagoras. (Connected Mathematics), Dale
Seymour Publications © 1998