Question

CHALLENGE GEOMETRY QUESTION!!

Derive a formula that can find the perimeter of a n(any number of sides) gon. Using only number of sides and Apotham.

Answer 1

Is the polygon of n sides a regular polygon?

Answer 2

yes. The polygon can create a triangle

Answer 3

Create a triangle? What do you mean?

Answer 4

Also, have you learnt trigonometric ratio as well as sum of angle in a polygon yet?

Answer 5

From the center of the polygon, it can create an apotham, radius, and half the side of the polygon creating a triangle

Answer 6

Sohcahtoa

Answer 7

180/n, (n-2)90/n yes

Answer 8

Ok! Then let's start.
Let us first consider a regular pentagon as an example. We'll generalize it as we proceed.

Forgive my poor drawing, what is the value of EACH interior angle of this regular pentagon?

Answer 9

360/5

Answer 10

but see, i'm trying to derive a formula not just solve for the perimeter :/

Answer 11

essentially create a formula so that if a problem was given just the number of sides, and apotham, you could insert the numbers into the formula finding the perimeter

Answer 12

We'll get there :)

Answer 13

Each interior angle of a pentagon is 360/5.
Similarly, each interior angle of a n-gon is 360/n, where n is the number of sides.
Agree?

Answer 14

yes

Answer 15

Ehmm, hold on... something's wrong.
Sum of interior angle of a n-sided polygon is NOT 360 degrees, but is (n-2)x360