Does a pentagon make 5 equilateral triangles?

Answer 1

A regular pentagon (one where all sides are equal and all central angles are equal) will not form five equilateral triangles (five triangles of equal side length).

The reason is if you make a point in the very centre of the pentagon and were to draw a line to each of the outside corners you would end up with five triangles, but if you look solely at the centre point you would see all of its surrounding sides have angles. This means that the sum of all those interior angles you just made would be 360 degrees (a full circle). Now if you divide that by the five segments you discover that each of the interior angles (the ones around the centre point) are actually 72 degrees.

Then using the knowledge that triangles have 180 degrees, you find that the other angles of your five triangle sections are actually 54 degrees.

An equilateral triangle would have all sides equal and all of its angles would be 60 degrees. This is not the case here and if you do some further math you discover that the outside sides of the pentagon are longer than the sides of your triangle segments as a result (they're actually an isosceles triangles).

If you can find the area of one triangle segment then you can get the area of the pentagon, this is just something to keep in mind when you're finding the area.

Hope that's alright, I literally just finished a question like this in my homework.