# Pg 24, q51. How do I figure this out? thanks

Consider for the

For symmetry reasons, the area of the polygon is

Moreover the triangle is isosceles and the angle at the top is:

so that we can see that the height of the triangle is:

while the length of the side is:

The area of the triangle is then:

and the area of the polygon is:

If we write this as:

We can see that as

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See below

The regular polygons are able to be split into equal isosceles triangles.

However, we need to total area.

This effect can be explored further, using just a value for the angle, here. Keep in mind that the notes sections don't allow for formatting, i.e. fractions.

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To provide assistance with page 24, question 51, I would need more context. Please provide the specific details or content of question 51 from page 24, and I'll be happy to help you figure it out.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- A triangle has corners at #(5 ,6 )#, #(4 ,3 )#, and #(2 ,5 )#. What is the area of the triangle's circumscribed circle?
- A circle's center is at #(3 ,1 )# and it passes through #(4 ,2 )#. What is the length of an arc covering #( pi ) /6 # radians on the circle?
- Points #(2 ,2 )# and #(8 ,1 )# are #(5 pi)/3 # radians apart on a circle. What is the shortest arc length between the points?
- A triangle has vertices A, B, and C. Vertex A has an angle of #pi/8 #, vertex B has an angle of #(pi)/12 #, and the triangle's area is #12 #. What is the area of the triangle's incircle?
- A triangle has vertices A, B, and C. Vertex A has an angle of #pi/2 #, vertex B has an angle of #( pi)/3 #, and the triangle's area is #56 #. What is the area of the triangle's incircle?

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