# How Well Can You Measure?

Warmup

Activity #1

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

Remember that a square has all the sides equal. So a diagonal drawn either from top left to bottom right, or from top right to bottom left, will measure the same. • Use the segment tool , to draw the diagonal of each square in the applet below.
• Use the distance tool , to measure the diagonal of each square. Record your measurements in the table below.
• Use to measure the perimeter of the square. Record your measurements in the table below.

• Plot the diagonal and perimeter values from the table on the coordinate plane given below.

(1.) What do you notice about the points on the graph?

• In the table below, record the length of the diagonal for each of the squares from the previous activity.

(2.) Then, calculate the area of each of your squares.

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

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

(4.) 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?

(5.) How is it different?

Activity #2

How to Measure Angles.

A protractor is the instrument used to measure angles. It 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. • Since the line AG, in the interactive model below is already aligned with the 0 on the inner scale, just use the blue circle to move AF along the protractor and observe how the angle changes.

Angles can be classified by their measures as follows:

(i.) A right angle has a measure of 90.

(ii.) An acute angle has a measure between 0 and 90.

(iii.) An obtuse angle has a measure between 90 and 180.

(iv.) A straight angle has a measure of 180.

In the following exercise, you are going to use the virtual protractor in the applet 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.

Activity #3

Try to score as many points as you can in this activity. • 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.

Challenge #1

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?

Challenge #2

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

Challenge #3

Quiz Time