What is a Heptagon?

A heptagon is a 7-sided polygon with 7 inner angles that amount to 900°. The name heptagon derives indigenous the Greek words hepta- because that seven and gon- because that sides. A disappearance is also called a 7-gon or septagon (septa- is Latin for seven).

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Heptagon Shape

The heptagon form is a aircraft or two-dimensional shape consisted of of 7 straight sides, seven internal angles, and also seven vertices. A heptagon shape can be regular, irregular, concave, or convex.


Here are some extr properties the the heptagon shape:

All heptagons have actually interior angles that amount to 900°All heptagons have exterior angle that sum to 360°All heptagons have the right to be divided into 5 trianglesAll heptagons have actually 14 diagonals (line segment connecting vertices)

Heptagon Sides

Heptagon sides should be straight and meet to kind seven vertices that close in a space. The 7 sides that a heptagon meet, however do not intersect, or cross over each other.


As with other 2d shapes, a heptagon"s sides can be various lengths, which create an rarely often rare heptagon. Or the sides can be congruent to kind a regular heptagon

A heptagon through sides that intersect is dubbed a heptagram.

Heptagon Angles

A heptagon has actually seven interior angles that sum to 900° and seven exterior angle that sum to 360°. This is true for both regular and irregular heptagons.


In a constant heptagon, each interior angle is roughly 128.57°.

Below is the formula to uncover the measure up of any kind of interior angle of a continuous polygon (n = number that sides):

180°n - 360°n

We recognize that every heptagons (or septagons) have 7 sides, therefore we have the right to plug that into our formula:(180° × 7) - 360°7 =

1260° - 360°7 =

900°7 ≈ 128.5714°


Heptagon Diagonals

Heptagons have 14 diagonals. For convex heptagons, all diagonals will be inside the shape. For concave heptagons, at the very least one diagonal will certainly be outside of the shape.


Regular Heptagon

Here is a photo of a regular heptagon. A continual heptagon has actually seven congruent sides, seven vertices, and seven congruent internal angles:


As suggested by the hash marks, the regular heptagon in the snapshot above has actually equal sides.

Convex Heptagon

A consistent heptagon is constantly a convex heptagon. A convex heptagon has no internal angles greater than 179°:


Since no internal angle is greater than 179°, no diagonal have the right to lie external the polygon.

Irregular Heptagon

Here is an rarely often, rarely heptagon, meaning its 7 sides space not congruent and its seven interior angles space not identical:


Like various other irregular polygons, irregular heptagons deserve to be convex or concave like the heptagon image above.

Concave Heptagon

A concave heptagon has at least one interior angle better than 180°, and it contends least one diagonal that lies external the polygon:


Area the A Heptagon

The area the a regular heptagon have the right to be uncovered using this formula:

This formula is approxmiatly equal to A = 3.643a2In both formulas, a = side length.

Heptagon In real Life

There are many examples of disappear in actual life, such as the two pictures below:


Like other geometric shapes, such as the octagon, hexagon, and also quadrilateral, heptagonal numbers can be uncovered in synthetic objects and also in nature.

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Heptagon Quiz

For any type of heptagon, what is the sum of its internal angles?For any kind of heptagon, how countless vertices does it have?For any kind of heptagon, how numerous diagonals deserve to you attract on it?Can a heptagon have nine sides?Below room some polygons. First, choose all that room heptagons. Then, for each heptagon girlfriend select, identify if that is consistent or irregular, and also then even if it is it is concave or convex:


Please try the work before you take a peek at the answers!

The internal angles that a disappear always include up come 900°.All heptagons have seven vertices, just as they have actually seven sides and seven interior angles.All heptagons will have actually 14 diagonals; if a diagonal lies exterior the polygon, you recognize the disappear is concave.


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What friend learned:

After working your method through this lesson and video, you should have actually learned:

What a heptagon form looks likeHow numerous sides, angles, and also diagonals a disappearance hasHow countless degrees are in a heptagonThe properties of both regular and also irregular heptagonsThe difference in between convex and concave heptagons