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Geometry Ch14.3 #16, #17, #34

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.