Question from Jackson:
I am on chapter 14 in geometry learning about the areas of regular polygons. I am having trouble understanding how they got the answers. Ex: 14.3 #16-19 I don’t know how to relate r to a. Are they talking in terms of the area of the square? I saw the answer and I have no Idea how they got to a square root.
Also, later in the lesson #34 and the others talking about relations, I just can’t grasp the concepts of relating the terms.
Thank you for your help.
Answer from Dr. Callahan:
For #17: Based on the other problems, you should see that this is a right triangle and PB = a. So both sides the same, or a 45-45-90 degree triangle.
So by pythagorean theorem
a^2 + b^2 = c^2
but in this case it is a^2 + a^2 = r^2
so we have 2a^2 = r^2
For number 16, now to get in terms of r, just solve for r by taking square root.
for 34, based on the two problems above, you know area of a triangle is 1/2 of its height times its base. But since you have two triangle of same area in the WHOLE triangle, you now have area of AOB
= a * r/2
and r/2 was equal to that in last problem – so multiply out.