![]() ![]() The concave pentagon below can be broken into a rectangle and two triangles. The pentagon below can be broken into 3 triangles. Note that there are other formulas for the area of a triangle. The area for a triangle is A = ½ × base × height. The formula for the area of a rectangle is A = length × width. The above pentagon can be broken down into a rectangle and a triangle, as indicated by the dotted lines. However, we would still need to know or be able to find the dimensions of various parts of the pentagon, so this method may not always be possible. Depending on the shape of the pentagon, we may be able to break it down into 3 triangles, a rectangle and a triangle, a rectangle and 2 triangles, and so on. The area of an irregular pentagon can be found by breaking the pentagon up into different polygons, calculating the areas of the respective polygons, then finding the sum of the areas. Note that apothems only exist for regular polygons. The figure below shows the apothem of a pentagon. The apothem of a regular pentagon is the length of the perpendicular line segment formed between the center of the pentagon and one side of the pentagon. For a regular pentagon, the perimeter is p = 5 × s. The perimeter of a pentagon is the sum of the length of its sides. The area of a regular pentagon can be calculated using a different formula if the length of a side and apothem are known: This formula can be used as long as one side length is known. The area of a regular pentagon formula with side length s is: This means that it can be rotated in such a way that it will look the same as the original shape 5 times in 360°. ![]() Symmetry in a regular pentagonĪ regular pentagon has 5 lines of symmetry and a rotational symmetry of order 5. Since the sum of the interior angles of a triangle is 180°, the sum of the interior angles of the pentagon is 3 × 180° = 540°. The sum of the interior angles of the three triangles equals the sum of interior angles of the pentagon. The blue lines above show just one way to divide the pentagon into triangles there are others. The sum of the interior angles of a pentagon equals 540°.Īs shown in the figure above, two diagonals can be drawn to divide the hexagon into three triangles. A total of five diagonals can be drawn for a pentagon. Two diagonals can be drawn from each vertex. Since each of the interior angles in a regular pentagon are equal in measure, each interior angle measures 540°/5 = 108° as shown below.Ī diagonal is a line segment joining two non-consecutive vertices.5 sides with equal measure that do not intersect and form a closed shape.Īll pentagons have interior angles that sum to 540° and exterior angles that sum to 360°.Properties of regular pentagonsĪ regular pentagon is a pentagon whose sides are equal in length, and whose interior angles are equal in measure it has the following properties. Note that the above does not consider self-intersecting pentagons, which are referred to as pentagrams. 5 sides that do not intersect and form a closed shape.The figure below shows an example of a convex and concave pentagon:īelow are some properties of all pentagons as well as properties specific to regular pentagons. Convex pentagon - all interior angles of the pentagon measure 180°.Pentagons can be classified as either convex or concave on top of being classified as regular or irregular. The figure below shows an example of a regular and irregular polygon: Irregular pentagon - not all sides and interior angles are equal.Regular pentagon - all sides and interior angles are equal.Like other polygons, a pentagon can be classified as regular or irregular. Pentagons are classified as either regular or irregular and concave or convex. The figure below shows an aerial view of The Pentagon, outlined in red. it is one of the world's largest office buildings and it is in the shape of a pentagon. One famous example of a pentagon is The Pentagon, near Washington, D.C. The figure below shows 3 examples of what a pentagon looks like: Pentagon shapeĪ pentagon is a five-sided polygon there are a few different pentagon shapes. In geometry, a pentagon is a closed 2D shape that has 5 sides and 5 angles. Home / geometry / shape / pentagon PentagonĪ pentagon is a five-sided polygon. ![]()
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