Area of Pentagon
The area of the pentagon is the area that is enclosed by all five sides of the pentagon. A pentagon is a fivesided polygon in which a twodimensional geometrical figure and its name are derived from Greek words "Penta" which meant "five" and "gon" which meant "angles". In this lesson, we will learn about the area of the pentagon with solved examples and practice questions. Stay tuned to explore more!!!
1.  What is the Area of Pentagon? 
2.  Area of Pentagon Formula 
3.  Calculation of Area of Pentagon 
4.  FAQs on Area of Pentagon 
What is the Area of Pentagon?
The area of the pentagon is the area that is within the sides of the pentagon. A pentagon has 5 diagonals, and the sum of its interior angles of the pentagon equals 540° also, the sum of its exterior angles equals 360°. The area of the pentagon can be calculated by diving it into 5 equal isosceles triangles. To calculate the area of the pentagon we can use the area of an isosceles triangle. We divide the area of the pentagon into five isosceles triangles and calculate it accordingly. The formula for the area of the pentagon in terms of the side is \frac{1}{4}\sqrt{5(5+2\sqrt{5})}s^{2}\) and in terms of side (s), apothem (a) the area is 5/2 × s × a where a is the apothem length, and s is the side of the pentagon. The area of the pentagon is expressed in square units like m^{2}, cm^{2}, in^{2}, or ft^{2}, etc.
Area of Pentagon Formula
Consider a pentagon having side "s" and length of apothem "a". The area of the Pentagon is equal to 5/2 times the apothem length and of the side of the Pentagon. The formula for the area of the pentagon is 5/2 × s × a.
The area of a regular pentagon can similarly be expressed in terms of length of side "s". Area of a regular pentagon, \(A = \frac{1}{4}\sqrt{5(5+2\sqrt{5})}s^{2}\) where "s" is the length of one side of a regular pentagon.
Calculation of Area of Pentagon
The area of a pentagon is 5/2 × s × a. By following the steps mentioned below we can find the area of the pentagon.
 Step 1: Calculate the length of the side of the pentagon.
 Step 2: Find the apothem length of the pentagon.
 Step 3: Find out the product of the 5/2 times the apothem length and of the side of the pentagon. This will give the area of the pentagon.
 Step 4: Represent the answer in square units.
Example: Find the area of the pentagon whose length of the side is 18 units and the length of apothem is 5 units.
Solution: Given that s = 18 units and a = 5 units
Thus, the area of the pentagon, A = 5/2 × s × a
⇒ A = 5/2 × 18 × 5
⇒ A = 225 square units
The area of the pentagon is 225 square units.
Solved Examples on Area of Pentagon

Example 1: Find the area of the pentagon if the length of the side of the pentagon is 10 in, and having a length of apothem is 6.88 in.
Solution: Given s= 10 in and a = 6.88 in.
Using the formula for the area of the Pentagon,
A = 5/2 × s × a
⇒ A = 5/2 × 10 × 6.88
⇒ A = 172 in^{2}Therefore, the area of the pentagon is 172 square inches.

Example 2: Jack was given an area of a pentagon as 500 units square and having a side of 17 units. Can you help him find the length of the apothem of the pentagon?
Solution: Given A = 500 units square and s = 17 units
Using the formula for the area of the Pentagon,
A = 5/2 × s × a
⇒ 500 = 5/2 × 17 × a
⇒ a = 11.76 unitsTherefore, the length of the apothem of the Pentagon is 11.76 units.
FAQs on Area of Pentagon
What is the Area of the Pentagon?
The area of the pentagon is the area that is covered by all the sides of the pentagon. The area of the pentagon can be found in either case whether the pentagon is a regular pentagon or an irregular pentagon.
What is the Unit of Area of Pentagon?
The unit of area of the pentagon is expressed in square units, for example, m^{2}, cm^{2}, in^{2}, or ft^{2}, etc.
What is the Formula of Area of Pentagon?
The formula of area of the pentagon is given by the formula 5/2 × s × a where 's' is the length of the side of the pentagon and 'a' is the apothem of a pentagon.
How to Find the Area of Pentagon?
We can find the area of the pentagon using the following steps:
 Step 1: Find the length of the side of the pentagon.
 Step 2: Identify the apothem length of the pentagon.
 Step 3: Find the product of 5/2 times the apothem length and of the side of the pentagon.
 Step 4: This will give the area of the pentagon and we represent the answer in square units.
How to Find the Area of Regular Pentagon?
We can find the area of the regular pentagon using the following steps:
 Step 1: Find the length of the side of the pentagon.
 Step 2: Find the area of regular pentagon using the formula \(A = \frac{1}{4}\sqrt{5(5+2\sqrt{5})}s^{2}\) where "s" is the length of one side of a regular pentagon.
 Step 4: This will give the area of the regular pentagon and represent the answer in square units.
What Happens to the Area of Pentagon If the Length of the Side is Tripled?
The area of the pentagon is tripled if the length of the side is tripled as the "s" is substituted to "3s" in the formula A = 5/2 × s × a = 5/2 × (3s) × a = 3 × (5/2 × s × a) which gives three times the original area of the pentagon.
What Happens to the Area of Pentagon If the Length of Apothem is Halved?
The area of the pentagon is tripled if the length of the side is tripled as the "a" is substituted to "a/2" in the formula A = 5/2 × s × a = 5/2 × s × (a/2) = (1/2) × (5/2 × s × a) which gives half the original area of the pentagon.