Pentagon Definition

In geometry, a pentagon is a five-sided polygon with 5 straight sides and five interior angles that amount up come 540°. A pentagon form is a airplane figure, or flat (two-dimensional) 5-sided geometric shape.

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Properties the a Pentagon

Pentagons can be basic or self-intersection. The properties of a basic pentagon (5-gon) space it must have 5 straight sides that fulfill to create five vertices, yet do not self-intersect:

Pentagons have five straight sidesPentagons have five interior angles, which sum to 540°The five sides carry out not intersect
A self-intersecting continuous pentagon is dubbed a pentagram.


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Types that Pentagons

Types that Pentagons

The two species of pentagons in geometry are consistent pentagons and also irregdular pentagon.

Regular Pentagons

A regular pentagon need to have five congruent sides, 5 congruent internal angles, and congruent exterior angles:five congruent sides (sides of same length)five congruent inner angles (each measuring 108°)five congruent exterior angle of 72°
Regular pentagons carry out not have parallel sides.


Just like any type of regular polygon, going roughly a pentagon completes one complete circle, for this reason the exterior angle are uncovered by splitting 360° through the variety of sides, in this case, 360°5 = 72°.

Irregular Pentagons

Irregular pentagons deserve to be a convex pentagon or a concave pentagon, yet they should have five different-length sides.

Convex pentagon - No interior angles can be much more than 180°Concave pentagon - One interior angle the is higher 180°


A common example that a convex irregular pentagon is the home plate ~ above a baseball field.

All pentagons (regular and also irregular) room five-sided shapes, with five interior angles and also five exterior angles.

Examples the Pentagons

If girlfriend look because that a pentagon shape roughly you, you will surely discover it. Even if it is it is an rarely often rare pentagon through varying side lengths or a regular pentagon with equal sides and equal angles, over there are many real-life examples of pentagons:

The famous U.S. Department of defense structure in Washington D.C. (The Pentagon building)The residence plate on a baseball fieldSchool cross signsSections ~ above a soccer ball


When you uncover a five-sided shape, friend can define it together a pentagonal shape.

Perimeter and Area of a Pentagon

The perimeter of a pentagon is the distance about its five straight sides. Over there is a simple formula to uncover the perimeter that a regular pentagon if you recognize one next length.

To discover the perimeter that an rarely often rare pentagon, you should measure and add up the five sides.

A heat segment attracted from the center of a constant pentagon perpendicular to a side is referred to as the apothem. The apothem is supplied to calculate the area of a pentagon.

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The area, A, the a pentagon is the an are inside it"s five straight sides. Just how to uncover the area will rely on which kind of pentagon you have and also what info you know about your pentagon.

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Perimeter that a Pentagon

Lesson Summary

Now the you"ve completed this lesson. You have to know:

That a pentagon is a five-sided polygon with 5 anglesThe identifying nature of a pentagonThe different types of pentagons