Lesson: Polygons

Comment on Polygons

Can we assume a polygon to be regular if nothing is mentioned?
greenlight-admin's picture

No. If the question doesn't stated that the polygon is regular, we can't assume that it's regular.



I have a potential dumb question here: How can we assume that all the sides of convex polygon are equal?
greenlight-admin's picture

Question link: https://greprepclub.com/forum/length-of-a-side-of-regular-pentagon-with-...

Good question.
The word "regular" tells us that all sides are equal.
Without the word "regular," we wouldn't be able to make any conclusions about the lengths of the sides.


I think in the last class you mentioned that quadrilaterals have interior angles equal to 360deg?? How can it have sum less than 180deg?
greenlight-admin's picture

That's correct; the 4 angles in a quadrilateral will ALWAYS add to 360°.
So, to answer your second question, the angles in a quadrilateral CANNOT have a sum less than 180°.

Where do I say that the angles in a quadrilateral have a sum less than 180°?


please you mentioned that to find the sum of the angles in a polygon you subtract 2 for the number of sides and multiple by 180 and cited example with octagon having 6 triangles within it, how is the regular hexagon having 6 triangles in the last question of the reinforcement activities instead of 4 to validate its interior summing up to 720
greenlight-admin's picture

Question link: https://greprepclub.com/forum/given-figure-is-that-of-a-regular-hexagon-...

The 6 angles in a hexagon will add to 720 degrees.

In the my solution to the above question, I divide the regular hexagon into 6 equilateral triangles.

Notice that each equilateral triangle has one of its angles at the CENTER of the hexagon.
These six angles at the CENTER are not part of the angles in a hexagon. So, we can disregard them.
When we disregard them, we see that the angles add to 720 degrees.

Does that help?


Dear Brent,


From your solution to this question, can I infer that perimeter of a polygon inscribed in a circle will always be smaller than the circumference of the inscribing circle cause distance from one point to another along a straight line will be smaller than the distance along a curve?
greenlight-admin's picture

Absolutely! The perimeter of a polygon inscribed in a circle will always be less than the circumference of the inscribing circle.

Hi Brent,

For this I had approached in this way
As sum of the interioir angles=900
the 4 equal angles will be 900/4 = 225
so Qa = 225

Is this the right approach

greenlight-admin's picture

Question link: https://greprepclub.com/forum/in-a-particular-seven-sided-polygon-the-su...

Your approach yielded the correct answer, but it's not valid.
If each of the four angles were 225, then the other three angles would be 0 degrees (which is impossible)


I solved this problem by dividing the polygon into 4 right triangles and a rectangle, deriving the sides with the 30-60-90 rule, getting the areas and adding. Yielded the same answer. Is it a valid approach or would it get me in trouble in other problems?

greenlight-admin's picture

Question link: https://greprepclub.com/forum/what-is-the-area-of-the-figure-below-11775...

That's a perfectly valid approach. Nice work!

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