What is a Heptagon?

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

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Heptagon Shape

The heptagon form is a plane or two-dimensional shape comprised of 7 straight sides, seven inner angles, and also seven vertices. A disappear shape deserve to be regular, irregular, concave, or convex.


Here room some extr properties of the disappear shape:

All heptagons have actually interior angles that amount to 900°All heptagons have actually exterior angle that sum to 360°All heptagons can be divided into five trianglesAll heptagons have 14 diagonals (line segments connecting vertices)

Heptagon Sides

Heptagon sides have to be straight and also meet to form seven vertices that close in a space. The 7 sides that a disappear meet, however do no intersect, or cross end each other.


As with other 2d shapes, a heptagon"s sides have the right to be different lengths, which create an rarely often, rarely heptagon. Or the sides can be congruent to form a continual heptagon

A heptagon through sides that crossing is referred to as a heptagram.

Heptagon Angles

A heptagon has seven internal angles that sum to 900° and also seven exterior angle that amount to 360°. This is true because that both regular and also irregular heptagons.


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

Below is the formula to find the measure up of any kind of interior edge of a constant polygon (n = number of sides):

180°n - 360°n

We recognize that every heptagons (or septagons) have 7 sides, therefore we can plug that right 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. Because that concave heptagons, at the very least one diagonal will be outside of the shape.


Regular Heptagon

Here is a photo of a regular heptagon. A consistent heptagon has seven congruent sides, 7 vertices, and seven congruent internal angles:


As shown by the hash marks, the constant heptagon in the picture above has actually equal sides.

Convex Heptagon

A regular heptagon is constantly a convex heptagon. A convex heptagon has actually no inner angles better than 179°:


Since no inner angle is higher than 179°, no diagonal have the right to lie exterior the polygon.

Irregular Heptagon

Here is an rarely often rare heptagon, definition its seven sides room not congruent and also its seven internal angles space not identical:


Like other irregular polygons, rarely often rare heptagons have the right to be convex or concave like the heptagon photo above.

Concave Heptagon

A concave heptagon contends least one internal angle better than 180°, and it contends least one diagonal the lies exterior the polygon:


Area that A Heptagon

The area of a consistent heptagon deserve to be found using this formula:

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

Heptagon In real Life

There are numerous examples of disappear in actual life, such together the two images below:


Like other geometric shapes, such as the octagon, hexagon, and also quadrilateral, heptagonal numbers can be discovered in man-made objects and in nature.

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Heptagon Quiz

For any type of heptagon, what is the amount of its interior angles?For any type of heptagon, how many vertices does it have?For any kind of heptagon, how many diagonals deserve to you draw on it?Can a heptagon have nine sides?Below space some polygons. First, choose all that room heptagons. Then, because that each heptagon girlfriend select, recognize if it is consistent or irregular, and then whether it is concave or convex:


Please try the work prior to you take a emergence at the answers!

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


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What you learned:

After functioning your method through this lesson and also video, friend should have learned:

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