True
a regular pentagon or just a pentagon
yes True
108
pyramid
If the pentagon is a regular pentagon, then each of the central angles (formed by joinning the center with the vertices) is72⁰ (1/5 of 360⁰). So that 5 congruent isosceles triangle are formed, with base angles of 54⁰. If we draw the height, of these triangles (from the center to the sides of the pentagon), 10 congruent right triangles are formed. Let denote with: b the sides of the pentagon, and h the height. In one of the right triangles we have: tan 54⁰ = h/(b/2) tan 54⁰ = 2h/b 1.38 = 2h/b 2h = 1.38b h = (1.38/2)b h = .69b So that, h/b = .69b/b = .69
True.
If it is a regular pentagon then it will have 5 congruent sides.
A regular pentagon has 5 congruent sides
No, a regular pentagon cannot have congruent sides but non-congruent angles. By definition, a regular pentagon has all sides of equal length and all interior angles equal. In a regular pentagon, the angles are each 108 degrees, ensuring that both the sides and angles are congruent. If the sides are congruent but the angles are not, it would be classified as an irregular pentagon instead.
No. A small pentagon will have smaller diagonals than a large pentagon! However, all the diagonals of a regular pentagon will be congruent.
Not necessarily; if it is a regular pentagon, then yes.
yes.
true
If you mean the area of the regular hexagon, then the answer is yes.
No, but a regular pentagon is equilateral. Equilateral means that all sides are congruent (equal in measure); to be regular, all angles also have to be congruent.
a regular pentagon or just a pentagon
yes True