Class of Tueday, 28 of April

Today we started by learning how to solve for the area of regular polygons.




First, we solved for the area on the pentagon, on the sheet of paper that she gave us. Then, we solved for the area of the octagon, when she told us that the raduis of the circumscribed circle was 10. To solve:







y= i/2

a= apothem


x= side/2



(circumscribed circle means a cirle on the outside of the octagon that touches all the vertices of the octagon)



That means that the radius is one of the sides of a triangle made from the diagonals.


First, you have to calculate the sum of interior angles to find one interior angle, in order to find angle y:


si= 180(8-2) = 1080


i= 1080/8 = 135


y= 135/2 = 67.5

Now, we calculate the apothem:

sin 67.5= a/10

a= 9.238


Then we calculate x:


cos 67.5= x/10


x= 3.826 (remember always to use at least 3 decimal places)

Then calculate the base (side of the octagon):


b= 2x= 7.654


Then calculate the perimeter:


p= 8b = 61.229


then calculate the area:


A= (pXa)/2


A= (61.229X9.238)




A= 282.8u²


So here are the Formulas for the Area of Regular Polygon:





p= perimeter
a= apothem

(Area of Circles):