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.
(1.) What do you notice about the points on the graph?
(2.) Then, calculate the area of each of your squares.
(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?
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.
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.
More About Measuring Angles.
Try to score as many points as you can in this activity.
Here is a rough map of a neighborhood.
There are 4 mail routes during the week.
How long is the route on Thursdays?
Estimate the side length of a square that has a 9 cm long diagonal.