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The area of a regular pentagon can be found by breaking the pentagon into five congruent triangles and then taking the sum of their areas?
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∙ 14y ago
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∙ 14y ago
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The area of a regular heptagon can be found by breaking the heptagon into seven congruent triangles and then taking the sum of their areas?
yes True
A polygon with 5 congruent sides?
a regular pentagon or just a pentagon
How many triangles in a regular pentagon?
108
What is the ratio of the height to the sides of a pentagon?
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
Prove four vertices of pentagon are concyclic?
First make sure you understand that concyclic simply means the points lie on a common circle. We are not told it is a regular pentagon but we will assume it is. We could create pentagons that are not even convex and would not be concyclic.Let's start with a regular pentagon. You can split it up into 5 congruent triangles with the points meeting at the middle. Any side of one of these triangle is connected from each of the vertices of the pentagon to the center of the pentagon. Since all 5 triangles are congruent, this distance must be the same for each of the vertices. So, we see that each of the vertices is equidistant from a given point. Now if we drew a circle centered at that point with a radius equal to the distance between the point and any vertex, that circle would pass through all 5 vertices. Therefore any four ( really all 5), vertices of a regular pentagon are concyclic.A nice proof would use Ptolemy's theorem. I will place a line to an answers.com page that helps with that.Another solution:The pentagon has to be regular. Otherwise, the question is impossible to prove.Consider a regular polygon ABCDE.Take triangles BCD & ECDBC=ED (sides of a regular polygon are equal)CD=CD (common side)
True or False Can The area of a regular pentagon be found by breaking the pentagon into five congruent triangles and then taking the sum of their areas?
True.
How many congruent sides does a pentagon have?
If it is a regular pentagon then it will have 5 congruent sides.
How many congruent sides in a pentagon?
A regular pentagon has 5 congruent sides
Can The area of a regular hexagon be found by breaking the hexagon into six congruent triangles and then taking the sum of their areas?
yes.
The area of a regular hexagon can be found by breaking the hexagon into six congruent triangles and then taking the sum of their areas?
true
Can a regular hexagon be found by breaking the hexagon into six congruent triangles and then taking the sum of their areas?
If you mean the area of the regular hexagon, then the answer is yes.
Do all regular pentagons have congruent diagonals?
No. A small pentagon will have smaller diagonals than a large pentagon! However, all the diagonals of a regular pentagon will be congruent.
Does a pentagon have congruent sides?
Not necessarily; if it is a regular pentagon, then yes.
Is an equilateral pentagon regular?
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.
The area of a regular heptagon can be found by breaking the heptagon into seven congruent triangles and then taking the sum of their areas?
yes True
A polygon with 5 congruent sides?
a regular pentagon or just a pentagon
Does a regular pentagon have congruent angles?
Yes
