What is a Heptagon?

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

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Heptagon Shape

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


Here space some added properties the the heptagon shape:

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

Heptagon Sides

Heptagon sides should be straight and also meet to kind seven vertices the close in a space. The 7 sides of a disappearance meet, yet do not intersect, or cross over each other.


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

A heptagon with sides that intersect is dubbed a heptagram.

Heptagon Angles

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


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

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

180°n - 360°n

We recognize that every heptagons (or septagons) have actually 7 sides, for this reason we deserve 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, every diagonals will be inside the shape. For concave heptagons, at least one diagonal will certainly be external of the shape.


Regular Heptagon

Here is a photo of a regular heptagon. A continual heptagon has seven congruent sides, 7 vertices, and also seven congruent interior angles:


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

Convex Heptagon

A continual heptagon is always a convex heptagon. A convex heptagon has actually no internal angles higher than 179°:


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

Irregular Heptagon

Here is an irregular heptagon, definition its seven sides space not congruent and its seven internal angles are not identical:


Like other irregular polygons, irregular heptagons have the right to be convex or concave favor the heptagon image above.

Concave Heptagon

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


Area the A Heptagon

The area the a continual heptagon can 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 numerous examples of disappear in genuine life, such together the two images below:


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

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Heptagon Quiz

For any kind of heptagon, what is the sum of its inner angles?For any kind of heptagon, how countless vertices does the have?For any kind of heptagon, how plenty of diagonals have the right to you draw on it?Can a heptagon have nine sides?Below space some polygons. First, pick all that room heptagons. Then, for each heptagon you select, identify if it is constant or irregular, and then whether it is concave or convex:


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

The internal angles of a heptagon always include up come 900°.All heptagons have seven vertices, just as they have seven sides and also seven interior angles.All heptagons will have 14 diagonals; if a diagonal lies outside the polygon, you understand the heptagon is concave.


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What girlfriend learned:

After functioning your way through this lesson and also video, girlfriend should have learned:

What a heptagon shape looks likeHow plenty of sides, angles, and also diagonals a disappearance hasHow plenty of degrees room in a heptagonThe properties of both regular and also irregular heptagonsThe difference in between convex and concave heptagons