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How to Calculate the Area of Pentagon? Formula | Calculator | Derivation

Area of Pentagon

The amount of space occupied by the pentagon is called the Area of a Pentagon, where Pentagon is defined as a polygon which has 5 sides that are equal and also angles present in the pentagon are equal.

One can get solution of their question as How to Calculate the Area of Pentagon? On the below tuned page we have gathered Area of Pentagon Formula, Calculator and its derivation.

Area of Pentagon

Candidates should note that a pentagon is sectored into 5 similar triangles because the sum of the angles of each triangle is 180 degrees. Check out below tuned image to make it more clear:

Area of Pentagon


s is the side of the pentagon.

a is the apothem length.

How to Calculate the Area of Pentagon?

Step 1: Start with the side length and apothem

Step 2: Divide the pentagon into five triangles

Step 3: Calculate the area of a triangle

Step 4: Multiply by five to find the total area

Formula to Calculate Area, Perimeter, Circumference: Find Area of Circle

Question: Find the area of a pentagon of side 5 cm and apothem length 3 cm?

Solution: Given,
s = 5 cm
a = 3 cm

Area of a pentagon
= 5/2 sa
= 5/2 * 5 * 3 cm2
= 5 ∗ 5 ∗ 3 /  2 cm2
= 75 / 2 cm2
= 37.5 cm2

Question: Find the area of a pentagon of side 12 cm and apothem height 7 cm ?


s = 12 cm
r = 7 cm

Area of a pentagon
= 5/2 sa
= 5/2 * 12 * 7 cm2
= 5∗12∗7 / 2 cm2
= 420 / 2 cm2
= 210 cm2

How to Find: Area of Quadrilateral

Area of Pentagon Calculator

For the easiness of candidates, we have provided above Area of a Pentagon Calculator that will surely help you in solving the area of a five-sided pentagon. Well, Pentagon surface area is found by substituting the value of the side in the below given formula.

Check Also: Area of Polygon Formula

Area of Pentagon Derivation

A regular pentagon has five lines of reflectional symmetry, and rotational symmetry of order 5 (through 72°, 144°, 216° and 288°). The diagonals of a convex regular pentagon are in the golden ratio to its sides.

The area of any regular polygon is:

A: 1 / 2 Pr, where P is the perimeter of the polygon, and r is the in radius (equivalently the apothem). Substituting the regular pentagon’s values for P and r gives the formula

with side length t.

We hope the above provided stuff in concern of Area of Pentagon will be beneficial for your, candidates having any query must comment in the below tuned comment box, our experts of will surely solve it as soon as possible.

Get Maths Vedic/Basic Formulas Free List: Maths Formulas

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