What is a Heptagon?

A heptagon is a 7-sided polygon v 7 internal angles that amount to 900°. The surname heptagon derives from the Greek native hepta- because that seven and gon- because that sides. A disappearance is also called a 7-gon or septagon (septa- is Latin because that seven).

You are watching: How many triangles can a heptagon be divided into

*


Heptagon Shape

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

*

Here space some added properties of the disappearance shape:

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

Heptagon Sides

Heptagon sides must be straight and meet to type seven vertices the close in a space. The seven sides the a disappear meet, however do no intersect, or cross over each other.

*

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


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

Heptagon Angles

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

*

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

Below is the formula to uncover the measure up of any type of interior edge of a consistent polygon (n = number that sides):


180°n - 360°n

We understand that all heptagons (or septagons) have actually 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. Because that convex heptagons, all diagonals will be within the shape. Because that concave heptagons, at the very least one diagonal will certainly be exterior of the shape.

*

Regular Heptagon

Here is a picture of a regular heptagon. A continual heptagon has actually seven congruent sides, seven vertices, and also seven congruent inner angles:

*

As indicated by the hash marks, the regular heptagon in the photo above has equal sides.

Convex Heptagon

A consistent 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 deserve to lie exterior the polygon.

Irregular Heptagon

Here is an rarely often rare heptagon, definition its seven sides are not congruent and its seven interior angles are not identical:

*

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

Concave Heptagon

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

*

Area of A Heptagon

The area the a continuous heptagon have the right to 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 many examples of disappearance in genuine life, such as the two images below:

*

Like various other geometric shapes, such together the octagon, hexagon, and quadrilateral, heptagonal figures can be discovered in fabricated objects and also in nature.

See more: What Two Bodies Of Water Did The Erie Canal Connect Ed By The Erie Canal?

Heptagon Quiz

For any type of heptagon, what is the sum of its inner angles?For any type of heptagon, how plenty of vertices does the have?For any heptagon, how countless diagonals deserve to you attract on it?Can a heptagon have nine sides?Below room some polygons. First, pick all that are heptagons. Then, for each heptagon girlfriend select, determine if it is continual or irregular, and then whether it is concave or convex:

*

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

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

*

Next Lesson:

Decagon


What girlfriend learned:

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

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