Area Of A Pentagon Formula

Area of a Pentagon Formula

In Geometry, a pentagon is a polygon with five sides. Its shape could be simple or self-intersecting. The Greek words “Penta” and “gon,” which indicate “five” and “angles,” were combined to create the name. The Pentagon has identical angles at each of its five corners. Every side and angle of a regular pentagon are equal. Pentagons can be convex or concave, regular or irregular. One with equal sides and angles is referred to as a regular pentagon. It has 108 degrees of interior angles and 72 degrees of exterior angles. An irregular pentagon is a figure without defined angles because it lacks equal sides and/or angles. In contrast to a concave pentagon, which has vertices that point inside, a convex pentagon has vertices that point outward where the sides meet. In a straightforward pentagon, the interior angles add up to 540°. A pentagram is a self-intersecting regular pentagon (sometimes known as a star pentagon). A pentagon’s area is calculated using its sides and apothem length. A polygon with five equal-length sides is called an equilateral pentagon. It can, however, form a family of pentagons since its five internal angles can take a variety of sets of values. On the contrary, since it is equilateral and equiangular, the regular pentagon is distinct up to resemblance (its five angles are equal). A cyclic pentagon is one in which the circumcircle, a circle, passes through each of its five vertices. A sample of a cyclic pentagon is the conventional pentagon.

Area of a Pentagon

The space enclosed by a pentagon’s sides is referred to as the pentagon’s area. Various techniques can be used to compute the Area Of A Pentagon Formula depending on the dimensions that are known. The type of pentagon also makes a difference. For instance, if it is a normal pentagon, the area can be determined using a single Area Of A Pentagon Formula, but if it is an irregular pentagon, one must divide it into various polygons and add their areas to determine the pentagon’s total area. A pentagon’s Area Of A Pentagon Formula is measured in square units.

How to Calculate the Area of a Pentagon.

Depending on the data provided and the type of pentagon, many techniques and the Area Of A Pentagon Formula can be used to determine the area of a pentagon.

Area of a Regular Pentagon

Regular pentagons have inner angles of 108° and the Schläfli symbol 5. A regular pentagon possesses rotational symmetry of order 5 (through 72°, 144°, 216°, and 288°) and five lines of reflectional symmetry. The golden ratio describes how the diagonals of a convex regular pentagon relate to its sides. The Area Of A Pentagon Formula for finding the area of a regular pentagon that is frequently employed is,

Area of the pentagon = 1/2 p a

Here, “p” stands for the pentagon’s perimeter, while “a” stands for its apothem. One can see the apothem “a” and the side-length “s” in the following pentagon. Knowing the side length, one can determine the area of a regular pentagon.

The regular convex pentagon has an inscribed circle, like other regular convex polygons. The regular convex pentagon has a circumscribed circle, just as every other regular convex polygon. If P is any point on the circumcircle between points B and C for a regular pentagon with the vertices A, B, C, D, and E, then PA + PD = PB + PC + PE. With the use of a compass and straightedge, one can draw a regular pentagon in a given circle or build one on a given edge. Around 300 BC, Euclid described this procedure in his work titled “Elements”.

Area of an Irregular Pentagon

By breaking up an irregular pentagon into smaller polygons, the area of the irregular pentagon can be calculated. To determine the area of the pentagon, the areas of these polygons are calculated and summed up.

Solved Examples on Area of Pentagon

To fully comprehend the idea, students should practice numerous questions on the Area Of A Pentagon Formula. Students will be able to determine the Area Of A Pentagon Formula and use it while solving problems. On the Extramarks website and mobile application, there are a number of solved examples on the Area Of A Pentagon Formula for practice.

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FAQs (Frequently Asked Questions)

1. What is the Area Of A Pentagon Formula?

The Area Of A Pentagon Formula is

Area of the pentagon = 1/2 p a

where, “p” stands for the pentagon’s perimeter, while “a” stands for its apothem.

2. Where to find questions on the Area Of A Pentagon Formula?

Several questions on the Area Of A Pentagon Formula can be found on the Extramarks website and mobile application.