How Well Can You Measure?


Investigate the Relation Between the Diagonal, Area, and Perimeter of a Square.

For each square, measure the length of the diagonal and the perimeter of the square in centimeters. Record your measurements in the table. Use the segment and Distance tool in your measurements.

Plot the diagonal and perimeter values from the table above on the coordinate plane.

(1). What do you notice about the points on the graph? Record measurements of the other squares to complete your table.

In the table below, record the length of the diagonal for each of the squares from the previous activity. Next, calculate the area of each of your squares.

Plot the diagonal and area values from the table above on the coordinate plane.

(2). Examine the graph of these values. What do you notice? 

(3). How is the relationship between the diagonal and area of a square the same as the relationship between the diagonal and perimeter of a square from the previous activity? How is it different?


How to Measure Angles.

he protractor is the instrument used to measure angles. The protractor has two scales running from 0 to 180 degrees in opposite directions. To measure an angle, place the center point of the protractor on the vertex, then align the zero on either side of the scale with one side of the angle.

(A). Since AG, in the interactive model is aligned with the 0 on the inner scale, use the blue circle to move AF along the protractor and observe the value of the angle.

Angles can be classified by their measures as follows:

A right angle has a measure of 90.

An acute angle has a measure between 0 and 90.

An obtuse angle has a measure between 90 and 180.

A straight angle has a measure of 180.

(B). Use the virtual protractor in the applet below to measure the angle between the red lines. Use the red dot of the protractor to align 0 with one of the lines. Make sure that the lines converge at the perpendicular bisector of the protractor. After measuring the angle use the dropdown to select the angle. Then click to measure another angle.


More About Measuring Angles.

Try to score as many points as you can.

Use the red cross to move the protractor, and the green circle to rotate it.

After you enter an angle, press the Enter key. If the value is correct, you will receive an approval, otherwise it will say “No”. No point is deducted. Just keep trying until you have the correct value. Use the slider for a new angle.


Here is a rough map of a neighborhood.

There are 4 mail routes during the week.

  • On Monday, the mail truck follows the route A-B-E-F-G-H-A, which is 14 miles long.
  • On Tuesday, the mail truck follows the route B-C-D-E-F-G-B, which is 22 miles long.
  • On Wednesday, the truck follows the route A-B-C-D-E-F-G-H-A, which is 24 miles long.
  • On Thursday, the mail truck follows the route B-E-F-G-B.

How long is the route on Thursdays?


Estimate the side length of a square that has a 9 cm long diagonal.


Select all quantities that are proportional to the diagonal length of a square.