In geometry, a pentagon is a five-sided polygon with five straight sides and five interior angles that sum up to . A pentagon shape is a plane figure, or flat (two-dimensional) 5-sided geometric shape.
Pentagons can be simple or self-intersection. The properties of a simple pentagon (5-gon) are it must have five straight sides that meet to create five vertices, but do not self-intersect:
The two types of pentagons in geometry are regular pentagons and irregdular pentagon.
A regular pentagon must have five congruent sides, five congruent interior angles, and congruent exterior angles:
Just like any regular polygon, going around a pentagon completes one full circle, so the exterior angles are found by dividing by the number of sides, in this case, .
Irregular pentagons can be a convex pentagon or a concave pentagon, but they must have five different-length sides.
A common example of a convex irregular pentagon is the home plate on a baseball field.
All pentagons (regular and irregular) are five-sided shapes, with five interior angles and five exterior angles.
If you look for a pentagon shape around you, you will surely find it. Whether it is an irregular pentagon with varying side lengths or a regular pentagon with equal sides and equal angles, there are many real-life examples of pentagons:
When you find a five-sided shape, you can describe it as a pentagonal shape.
The perimeter of a pentagon is the distance around its five straight sides. There is a simple formula to find the perimeter of a regular pentagon if you know one side length.
To find the perimeter of an irregular pentagon, you must measure and add up the five sides.
A line segment drawn from the center of a regular pentagon perpendicular to a side is called the apothem. The apothem is used to calculate the area of a pentagon.
The area, , of a pentagon is the space inside it's five straight sides. How to find the area will depend on which type of pentagon you have and what information you know about your pentagon.
Now that you've completed this lesson. You should know:
In geometry, a pentagon is a five-sided polygon or 5-gon.
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