Find Area Of A Pentagon

The surface area of a pentagon is a region covered by all the sides of the pentagon. A pentagon is a two-dimensional shape in geometry. A pentagon is a v-sided polygon, besides called 5-gon. It can exist regular as well equally irregular. The sides and angles of a regular pentagon are equal to each other.

Theinterior angle equals 108 degrees, and its exterior angle is equal to 72 degrees. The sum of interior angles of the pentagon is 540° and the sum of exterior angles is 360°.

In this article, we will acquire the area of the pentagon for regular and irregular pentagon forth with formulas and examples.

What is Area of Pentagon?

The surface area of a pentagon is space covered by the sides of the pentagon in a plane. The unit of surface area of a pentagon is given by square unit of measurement, such as cm², m², in^two, etc.

Area of pentagon

Surface area of Pentagon Formula

Area of pentagon formula can be derived from three different methods.

Using the length of the side (in case of the regular pentagon)
Using the apothem
Using the area of an isosceles triangle

Area of Regular Pentagon

If the side of the regular pentagon is given, and so the expanse of the pentagon is given by:

Area of a pentagon,

\(\begin{array}{fifty}A = \frac{i}{4}\sqrt{v(five+2\sqrt{5})}southward^{2}\cease{array} \)

where southward is the side length of pentagon.

Surface area of Pentagon using Apothem

If the side-length and apothem is given of a pentagon, so;

Area of Pentagon = 5/2 x s x a;

where 's' is the side of the pentagon, and 'a' is the apothem length.

Area of pentagon formula

Apothem is the line from the center of the pentagon to a side, intersecting the side at xc degrees correct angle.

Area of Pentagon Using area of Isosceles triangles

If the pentagon is divided into five equal isosceles triangles, then nosotros tin can discover the area of an individual triangle and add them to become the area of the pentagon.

Surface area of pentagon = Sum of the expanse of five isosceles triangles formed within the pentagon

How to Find Surface area of Pentagon?

To find the area of a pentagon, divide the regular pentagon into five equal triangles. Each of the triangles is an isosceles triangle.

Area of pentagon derivation

By the formula of area of the isosceles triangle, when all 3 sides are given,

Expanse = A = ½[√(a² − bⁱⁱ⁄iv) × b]

where a is the length of equal sides and b is the base of the triangle.

Hence,

Area of Pentagon = 5 × Area of isosceles triangle

Perimeter of Pentagon Formula

The perimeter of a pentagon is the total length of its boundaries. Therefore, it is equal to the sum of all its 5 sides. For a regular pentagon, the perimeter is given by:

Perimeter of Pentagon

Example: If the side length of a regular pentagon is equal to 7 cm. Then find its perimeter.

Solution: Given, length of the side of the pentagon = 7 cm

Perimeter of pentagon = 5 ten side = 5 ten 7 = 35 cms

Diagonals of Pentagon Formula

The number of diagonals in a Pentagon is five.

Number of diagonals in any pentagon ={n*(n-3)}/2, where north = number of sides

In the case of the pentagon, the number of sides is equal to 5, northward = five.

Therefore, Number of diagonals of pentagon = [5(5-iii)]/2 = (5 x 2)/2 = 5

Related Manufactures

Angles In A Pentagon
Area Of Polygon
Area Of Quadrilateral
Surface area Of Isosceles Triangle
Expanse Of Trapezium

Solved Examples on Area of Pentagon

Example 1: Let'due south take the pentagon with a side length is 5 units and apothem length is ii units

Area of pentagon is = five/ii x s x a

= 5/2 x v x ii

=25 square centimetres.

Case ii: Discover the area of a pentagon of side 5 cm and apothem length 3 cm?

Solution :

Given,

s = v cm

a = 3 cm

Area of a pentagon

= 37.5 cm

Do Questions on Area of Pentagon

What is the area of the pentagon if the side length of a regular pentagon is 7 cm?
If the apothem is 2.five cm and the area of a pentagon is 100 sq.cm, notice the side length of a pentagon.

Frequently Asked Questions – FAQs

What is the area of pentagon?

The area of a pentagon is the region covered by its five sides in a plane.

What is the formula for area of pentagon with apothem?

If 's' is the side and 'a' is the apothem, then the area of pentagon is equal to v/2 ten due south 10 a.

How to derive the area of pentagon?

To derive the area of pentagon, carve up the regular pentagon into five equal isosceles triangles. Add together the expanse of all the triangles to get the area of pentagon.

Can we find the area of pentagon without knowing the length of its sides?

To notice the expanse of pentagon, nosotros have to know the length of its sides. Using apothem, we have expanse of pentagon equals to 5/2 ten s 10 a. Using merely sides of regular pentagon, the area will be 1/iv[√5(five+2√v))]s²