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Area of Pentagon

Area of Pentagon

A pentagon is a geometrical figure that consists of 5 sides. “Penta” denotes five while “gon” denotes angle. It is one type of polygon in which its sum of all the interior angles is 540. All five sides in a figure are supposed to intersect with each other to form a pentagon. Multiple pentagon shapes are available based on the angles, vertices, sides etc.

There are also different pentagon types based on their shapes. The first demarcation is known as regular and irregular, and the second one is concave and convex. In a regular pentagon, all the sides are the same in terms of length, along with the measures of the five angles. Meanwhile, an irregular one does not have the same side lengths and angle measures.

Area of Pentagon

Perimeter of a Pentagon

For a regular pentagon consists of five equal sides, given below is the formula for finding the perimeter: If the pentagon has a side equal to ‘s’, then,

The Perimeter of a Pentagon, P = 5 s units

From this formula, it can be easily understood that all five sides are congruent, so the perimeter is obtained by simply multiplying it by 5. Similarly, this pentagon is easily divided into five separate equilateral triangles. So, to calculate the area of a regular pentagon, it can be deemed equal to 5 times the area of the obtained equilateral triangle having a side length equal to that of the pentagon. A convex pentagon is obtained if every vertex of the pentagon is pointing outwards. In the meantime, if the pentagon has even one vertex directed inside, then this is called a concave pentagon.

Properties of a Pentagon

Some common properties need to be followed while constructing a pentagon. Those are;

  • The sum of the internal angles of the pentagon is equal to 540.
  • If all the sides are equal along with the angles, a regular pentagon is formed. If not, then it is irregular.
  • In regular ones, all the interior angles measure 108 and each exterior one measures 72. Equilateral pentagons have five equal sides.

Area of a Pentagon

The area of the pentagon is nothing but the amount of planar space occupied by the pentagon. Few terms need to be understood before going into studying the area and its formulae. A line segment drawn from the pentagon’s centre, which acts perpendicular to one of the pentagon sides, is known as apothem. Next, the radius of the pentagon can simply be obtained by extending the length of the measuring line from the centre to the vertex. A side of the pentagon is defined as the length of the side, whereas the perimeter is the addition of the length of all the sides.

  • The following is the simple formula is used to calculate the area of a regular pentagon, in which its sides and apothem length are known;
    Area of Regular Pentagon = 5/2 * Side Length * Apothem
  • If only the length of the side is known;
    Area = square units
  • If only the radius is given,
    Area = (5 / 2) square units


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