Heptagon Sum Of Interior Angles

What is a Heptagon?

A heptagon is a vii-sided polygon with 7 interior angles that sum to $900 °$ . The proper noun heptagon derives from the Greek words hepta- for seven and gon- for sides. A heptagon is also called a 7-gon or septagon (septa- is Latin for seven).

$What Is A Heptagon$

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What Is A Heptagon?
Heptagon Shape
- Sides
- Angles
- Diagonals
Regular Heptagon
- Convex Heptagon
Irregular Heptagon
- Concave Heptagon
Surface area Of A Heptagon
Heptagons In Real Life

Heptagon Shape

The heptagon shape is a aeroplane or 2-dimensional shape comprised of seven straight sides, seven interior angles, and seven vertices. A heptagon shape can be regular, irregular, concave, or convex.

$Heptagon Shape$

Here are some boosted properties of the heptagon shape:

All heptagons accept interior angles that sum to $900 °$
All heptagons accept exterior angles that sum to $360 °$
All heptagons tin be divided into five triangles
All heptagons have $14$ diagonals (line segments connecting vertices)

Heptagon Sides

Heptagon sides must exist directly and meet to form seven vertices that shut in a space. The seven sides of a heptagon meet, but exercise not intersect, or cross over each other.

$Heptaon Sides$

Equally with other 2d shapes, a heptagon's sides tin can be unlike lengths, which creates an irregular heptagon. Or the sides can be congruent to form a regular heptagon

A heptagon with sides that intersect is called a heptagram.

Heptagon Angles

A heptagon has seven interior angles that sum to $900 °$ and 7 exterior angles that sum to $360 °$ . This is true for both regular and irregular heptagons.

$Heptagon Angles$

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

Below is the formula to detect the measure of whatever interior angle of a regular polygon ( $north =$ number of sides):

We know that all heptagons (or septagons) have $7$ sides, so nosotros can plug that into our formula:

$\frac{((180 ° \times seven) - 360 °)}{7} =$

$\frac{(1260 ° - 360 °)}{7} =$

$\frac{900 °}{vii} \approx 128.5714 °$

$Heptagon Formula To Find Interior Angle Measure$

Heptagon Diagonals

Heptagons have $14$ diagonals. For convex heptagons, all diagonals volition be inside the shape. For concave heptagons, at to the lowest degree 1 diagonal will be exterior of the shape.

$Heptagon Diagonals$

Regular Heptagon

Hither is a picture of a regular heptagon. A regular heptagon has seven coinciding sides, 7 vertices, and seven congruent interior angles:

$Regular Heptagon$

Every bit indicated past the hash marks, the regular heptagon in the movie above has equal sides.

Convex Heptagon

A regular heptagon is always a convex heptagon. A convex heptagon has no interior angles greater than $179 °$ :

$Convex Heptagon$

Since no internal angle is greater than $179 °$ , no diagonal can lie outside the polygon.

Irregular Heptagon

Here is an irregular heptagon, pregnant its seven sides are not congruent and its seven interior angles are not identical:

$Irregular Heptagon$

Similar other irregular polygons, irregular heptagons tin can be convex or concave similar the heptagon image to a higher place.

Concave Heptagon

A concave heptagon has at least one interior angle greater than $180 °$ , and it has at least one diagonal that lies outside the polygon:

$Concave Heptagon$

Area Of A Heptagon

The surface area of a regular heptagon can be found using this formula:

This formula is approxmiatly equal to $A = 3.643 a^{2}$

In both formulas, $a = s i d e l e n g t h$ .

Heptagon In Existent Life

In that location are many examples of heptagon in real life, such as the 2 pictures below:

$Heptagons In Real Life$

Like other geometric shapes, such as the octagon, hexagon, and quadrilateral, heptagonal figures can exist institute in homo-made objects and in nature.

Heptagon Quiz

For any heptagon, what is the sum of its internal angles?
For whatever heptagon, how many vertices does information technology take?
For any heptagon, how many diagonals can you describe on it?
Can a heptagon have 9 sides?
Beneath are some polygons. Beginning, select all that are heptagons. Then, for each heptagon you lot select, determine if it is regular or irregular, and and then whether information technology is concave or convex:

$Heptagon Quiz$

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

The interior angles of a heptagon ever add up to $900 °$ .
All heptagons accept seven vertices, but as they accept seven sides and seven interior angles.
All heptagons volition have $14$ diagonals; if a diagonal lies exterior the polygon, you know the heptagon is concave.
No, heptagons only have 7 sides. A ix sided polygon is chosen a nonagon.
Of the viii figures, just 5 are heptagons. Two are regular convex heptagons. Three are irregular concave heptagons. Bonus: ane shape in the filigree is a pentagon.