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Pentagon – Definition, Examples | EDU.COMEDU.COMResourcesBlogGuidePodcastPlanBackHomesvg]:size-3.5">Math Glossarysvg]:size-3.5">PentagonPentagon – Definition, ExamplesTable of ContentsPentagon Definition of Pentagon

A pentagon is a 2D polygon with five sides and five angles. The term "pentagon" originates from the Greek words "penta" meaning "five" and "gon" meaning "angles". A pentagon has five sides, five vertices (corners where two sides meet), five interior angles, five exterior angles, and five diagonals. The sum of all interior angles in any pentagon equals 540°. In a regular pentagon, each interior angle measures 108° and each exterior angle measures 72°.

Pentagons can be classified into four types based on their sides, angles, and vertices. A regular pentagon has all sides equal in length and all angles equal in measure, while an irregular pentagon has unequal sides and angles. A convex pentagon has all vertices pointing outward, while a concave pentagon has at least one vertex pointing inward (creating a bowl-like shape between some sides). The area of a regular pentagon can be calculated using the formula: Area = 12\frac{1}{2}21​ × Perimeter × Apothem, where apothem is the perpendicular distance from the center to any side.

Examples of Pentagon Example 1: Finding the Area of a Regular Pentagon Problem:

Neal measures a regular pentagon and finds that its side is 8 feet and the apothem is 6 feet long. How will he find its area?

Regular pentagon

Step-by-step solution:

Step 1, Write down the given measurements from the problem.

Apothem = 6 feet Side = 8 feet

Step 2, Recall the formula for the area of a regular pentagon.

Area of Regular Pentagon = 12\frac{1}{2}21​ × perimeter × apothem

Step 3, Calculate the perimeter of the pentagon by multiplying the side length by 5 (since a pentagon has 5 sides).

Perimeter = 5 × 8 = 40 feet

Step 4, Substitute the values in the area formula.

Area = 12\frac{1}{2}21​ × 40 × 6 Area = 12\frac{1}{2}21​ × 240 Area = 120 square feet Example 2: Calculating Pentagon Area with Different Measurements Problem:

If a regular pentagon has the side length of 10 cm and an apothem of 5 cm, find its area.

Regular pentagon

Step-by-step solution:

Step 1, Note the given values in the problem.

Length of side = 10 cm Length of apothem = 5 cm

Step 2, Apply the area formula for a regular pentagon.

Area of Regular Pentagon = 12\frac{1}{2}21​ × perimeter × apothem

Step 3, Find the perimeter by multiplying the side length by 5.

Perimeter = 5 × 10 = 50 cm

Step 4, Calculate the area by substituting the values.

Area = 12\frac{1}{2}21​ × 50 × 5 Area = 12\frac{1}{2}21​ × 250 Area = 125 square centimeters Example 3: Finding the Side Length of a Pentagon Problem:

If the perimeter of a regular pentagon is 200 cm, what would be the length of each side?

Regular pentagon

Step-by-step solution:

Step 1, Remember that a regular pentagon has 5 equal sides.

Step 2, Set up an equation using the definition of perimeter.

Perimeter = 5 × side length 200 cm = 5 × side length

Step 3, Solve for the side length by dividing both sides of the equation by 5.

Side length = 200 ÷ 5 Side length = 40 cm

Step 4, Check your answer: 5 sides of 40 cm each gives a perimeter of 200 cm, which matches the problem statement.

Comments(6)LLifeCoachMiaNovember 6, 2025I've used this pentagon def for my kid's study. Clear & helpful! Understanding types & area calcs made geometry fun.

NNatureLover85September 17, 2025This page was super helpful! I used the pentagon definition and examples to explain geometry to my daughter, and she finally got it. The step-by-step area calculation was a game-changer!

NNatureLover95September 10, 2025This glossary page on pentagons was super helpful for my 5th grader's homework! The clear examples made it easy to explain the difference between regular and irregular pentagons. Thanks for making geometry less intimidating!

MCMs. CarterAugust 27, 2025I’ve used the pentagon definition and examples from this page to help my kids with their geometry homework. The clear explanations and step-by-step area calculations really made it easy for them to understand!

MCMs. CarterAugust 20, 2025I used this page to explain pentagons to my daughter, and the clear examples made it so easy for her to understand! The step-by-step area calculation was a bonus for her homework too. Thanks!

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