Vertical Nonpermanent Surfaces Lesson

 

Finding the Area of a Regular Polygon

 

Prerequisites: chord, area of a triangle formula,

 

1) Draw a fairly large circle with center P.

2) Draw a radius PA that is 10 units.

3) Draw a chord from point A to another point B on the circle that is also 10 units in length.

4) Draw a chord BC congruent to chord AB.

5) Draw a chord CD congruent to chord AB.

6) ASK: What do you notice?

                ***Pass the marker***

7) Draw a chord DE congruent to chord AB.

8) Draw a chord EF congruent to chord AB.

9) Draw chord FA.

10) ASK: What shape is ABCDEF? (hexagon) What is the measure of each angle? (120)

11) Write the angle measure for each angle. What do you notice about the angles? What do you notice about the sides.

11) Write regular hexagon next to the figure. Discuss regular polygon.

12) Mark all sides congruent.

13) Draw PB. How long is PB? (10 units) How do you know?

***Pass the marker***

14) Find the area of triangle APB? (253 sq units)        ***Give a lot of time and make sure to give hints here***

15) Knowing the area of triangle APB, what else can we find?

16) Find the area of hexagon ABCDEF.   (1503 sq units)        

17) Find the altitude of triangle APB drawn from P and label this the apothem. The apothem of a regular polygon is a segment from the center of the polygon to the midpoint of a side.

18) Write A = ½ * 10 * 5 √3*6. What do each of these number represent?

19) Write A = ½ * s * a * n. What do each of the letters represent?

20) What can s * n be replaced with?

21) Write the formula for the area of the regular hexagon using only a and P for perimeter.