What is a Pentagon? - Shape, Area & Definition

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  • 0:00 The Pentagon: Not Just…
  • 1:10 Finding The Area Of A Pentagon
  • 1:25 Formula
  • 1:45 Example 1
  • 2:20 Example 2
  • 2:55 Lesson Summary
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Lesson Transcript
Instructor: Mimi Brestowski
This lesson will prepare you to work with pentagons by teaching you the definition, description of the geometric shape, and the formula for finding its area.

The Pentagon: Not Just a Building?

You may have heard of the government building called the 'Pentagon' but it's only a nickname. The building, which in fact is shaped like a pentagon, houses the US Department of Defense headquarters.

US Dept of Defense Headquarters (The Pentagon)

Definition and Description of a Pentagon

As you can see from the picture, a pentagon is a closed and flat two-dimensional surfaced shape with five angles and five sides. The word pentagon itself tells you what it is. 'Penta' is the Greek word for five and 'gonia' is the Greek word for angle. As already mentioned, the sides must be straight and closed. If there are any curves or lines that do not connect in the shape, it is not a pentagon.

Pentagons can be regular or irregular and convex or concave. A regular pentagon is one with all equal sides and angles. Its interior angles are 108 degrees and its exterior angles are 72 degrees. An irregular pentagon is a shape that does not have equal sides and/or angles and therefore do not have specified angles.

A convex pentagon is one whose vertices, or points where the sides meet, are pointing outwards as opposed to a concave pentagon whose vertices point inwards. Imagine a collapsed roof of a house.


Finding the Area of a Pentagon

In order to find the area of a pentagon, you will need to know the length of the sides and the apothem. The distance of each side is represented by s. The distance between the center and a side called the apothem is represented by a.


The formula to find the area of a regular pentagon is 1/2 times the perimeter of the pentagon times the apothem. Since the formula for the perimeter of a pentagon is 5s (five times the length of one side) and apothem is represented by a, our formula now looks like this:

Area = 1/2 * (5s) * a

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