how do you find the 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 5-sided polygon, too called 5-gon. Information technology tin be regular every bit well as irregular. The sides and angles of a regular pentagon are equal to each other.
Theinterior bending 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 learn the area of the pentagon for regular and irregular pentagon along with formulas and examples.
What is Area of Pentagon?
The area of a pentagon is space covered by the sides of the pentagon in a plane. The unit of area of a pentagon is given by square unit, such as cmii, thousandtwo, in2, etc.
Area of Pentagon Formula
Area of pentagon formula tin can be derived from three dissimilar 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, then the surface area of the pentagon is given past:
Area of a pentagon,
\(\begin{array}{l}A = \frac{one}{four}\sqrt{5(5+2\sqrt{5})}s^{2}\stop{array} \)
where southward is the side length of pentagon.
Area of Pentagon using Apothem
If the side-length and apothem is given of a pentagon, then;
Surface area of Pentagon = v/2 10 s x a;
where 's' is the side of the pentagon, and 'a' is the apothem length.
Apothem is the line from the eye of the pentagon to a side, intersecting the side at 90 degrees correct angle.
Expanse of Pentagon Using area of Isosceles triangles
If the pentagon is divided into 5 equal isosceles triangles, then we can discover the area of an individual triangle and add together them to get the area of the pentagon.
Area of pentagon = Sum of the area of five isosceles triangles formed within the pentagon
How to Find Area of Pentagon?
To find the expanse of a pentagon, divide the regular pentagon into five equal triangles. Each of the triangles is an isosceles triangle.
By the formula of area of the isosceles triangle, when all iii sides are given,
Surface area = A = ½[√(a2 − b2⁄4) × b]
where a is the length of equal sides and b is the base of the triangle.
Hence,
Area of Pentagon = five × Area of isosceles triangle
Perimeter of Pentagon Formula
The perimeter of a pentagon is the full length of its boundaries. Therefore, it is equal to the sum of all its five sides. For a regular pentagon, the perimeter is given by:
Example: If the side length of a regular pentagon is equal to 7 cm. Then detect its perimeter.
Solution: Given, length of the side of the pentagon = vii cm
Perimeter of pentagon = five x side = v x seven = 35 cms
Diagonals of Pentagon Formula
The number of diagonals in a Pentagon is five.
Number of diagonals in whatever pentagon ={n*(n-3)}/ii, where n = number of sides
In the example of the pentagon, the number of sides is equal to five, north = five.
Therefore, Number of diagonals of pentagon = [5(5-iii)]/2 = (5 x 2)/2 = v
Related Articles
- Angles In A Pentagon
- Area Of Polygon
- Area Of Quadrilateral
- Area Of Isosceles Triangle
- Area Of Trapezium
Solved Examples on Area of Pentagon
Case 1: Permit's take the pentagon with a side length is 5 units and apothem length is 2 units
Area of pentagon is = five/2 x s x a
= 5/ii x v x 2
=25 square centimetres.
Example two: Find the area of a pentagon of side 5 cm and apothem length 3 cm?
Solution :
Given,
s = 5 cm
a = iii cm
Surface area of a pentagon
= 37.v cm
Do Questions on Surface 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 ii.5 cm and the area of a pentagon is 100 sq.cm, observe the side length of a pentagon.
Often 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, and so the area of pentagon is equal to five/2 x s x a.
How to derive the area of pentagon?
To derive the area of pentagon, split up the regular pentagon into five equal isosceles triangles. Add the surface area of all the triangles to get the area of pentagon.
Can we observe the area of pentagon without knowing the length of its sides?
To find the area of pentagon, we have to know the length of its sides. Using apothem, nosotros have expanse of pentagon equals to 5/two ten s ten a. Using only sides of regular pentagon, the area will be 1/iv[√5(5+2√v))]southward2
Source: https://byjus.com/maths/area-of-pentagon/
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