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Pentagon

✨ The five-walled house

A pentagon is a flat geometric shape with five straight sides, five vertices, and five interior angles. The name comes from Greek words meaning “five” and “angle.” Like every polygon, a pentagon is a closed figure made of straight line segments.

Its five sides do not have to be the same length, and its angles do not have to be equal, so pentagons can have many different forms. A pentagon may be convex, with all its corners pointing outward, or it can have a more unusual concave form with one interior angle greater than 180 degrees.

These possibilities make the general pentagon different from the more specific regular pentagon. A regular pentagon has five sides of equal length and five equal interior angles. Each interior angle then measures 108 degrees, while the sum of all five interior angles is 540 degrees.

A regular pentagon also has five lines of symmetry, meaning that certain reflections leave its shape unchanged. The diagonals of a regular pentagon create interesting geometric patterns, including a five-pointed star when selected diagonals are drawn. Pentagons are studied in elementary geometry and can also be found in patterns, signs, designs, and some objects in everyday life.

💡 Did you know?

Did you know? The headquarters of the United States defense is a giant pentagon-shaped building. It is simply called 'The Pentagon'. It is so large that it has more than 28 kilometers of corridors, but thanks to its shape, one can go from one point to another in less than seven minutes!

Look closely at a classic soccer ball (the black and white model): it is composed of black pentagons surrounded by white hexagons. It is the assembly of these geometric shapes that allows the ball to be perfectly round and bounce everywhere!

If you draw a perfect five-pointed star without ever lifting your pencil from the sheet, you will see a small hidden pentagon appear in the center of the star. That's why mathematicians say that the pentagon and the star are like inseparable best friends!