What is a Heptagon?

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

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Heptagon Shape

The heptagon shape is a plane or two-dimensional shape consisted of of 7 straight sides, seven interior angles, and seven vertices. A disappear shape can be regular, irregular, concave, or convex.


Here are some extr properties of the disappearance shape:

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

Heptagon Sides

Heptagon sides need to be straight and also meet to kind seven vertices that close in a space. The 7 sides of a heptagon meet, but 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 rare heptagon. Or the sides have the right to be congruent to kind a constant heptagon

A heptagon v sides that intersect is referred to as a heptagram.

Heptagon Angles

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


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

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

180°n - 360°n

We know that every heptagons (or septagons) have actually 7 sides, for this reason we have the right to plug that right into our formula:(180° × 7) - 360°7 =

1260° - 360°7 =

900°7 ≈ 128.5714°


Heptagon Diagonals

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


Regular Heptagon

Here is a photo of a regular heptagon. A constant heptagon has actually seven congruent sides, 7 vertices, and seven congruent inner angles:


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

Convex Heptagon

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


Since no interior angle is higher than 179°, no diagonal deserve to lie exterior the polygon.

Irregular Heptagon

Here is an irregular heptagon, meaning its seven sides are not congruent and also its seven inner angles space not identical:


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

Concave Heptagon

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


Area that A Heptagon

The area that a constant heptagon can be uncovered using this formula:

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

Heptagon In genuine Life

There are numerous examples of disappear in genuine life, such as the two photos below:


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

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Heptagon Quiz

For any heptagon, what is the sum of its inner angles?For any type of heptagon, how countless vertices does it have?For any type of heptagon, how many diagonals deserve to you draw on it?Can a heptagon have nine sides?Below room some polygons. First, choose all that are heptagons. Then, for each heptagon you select, recognize if it is constant or irregular, and then even if it is it is concave or convex:


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

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


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What you learned:

After working your way through this lesson and also video, friend should have actually learned:

What a heptagon shape looks like How countless sides, angles, and diagonals a heptagon hasHow countless degrees space in a heptagonThe nature of both regular and also irregular heptagonsThe difference in between convex and also concave heptagons