Pentagon calculator is an online tool that is used to calculate the various properties of a pentagon. It can calculate the area, perimeter, diagonal, and side of a pentagon. This calculator makes the complex geometrical calculation very easy by offering the solutions at one click. We will discuss pentagon, its formulas, and much more in this space. If you are curious about pentagon calculations, keep reading because we are going to discuss several details about pentagon in this post.
Pentagon calculator not only eliminates the manual calculations but also provides a simple interface to make your calculations super-fast. To use this calculator, follow the below steps:
The area of pentagon calculator instantly calculates the properties of pentagon using the given values. It also provides the formula and step by step calculation using that formula. This calculator is very helpful for students who find geometry as a difficult topic. Students can learn the concept of a pentagon by using this calculator.
Pentagon is the five-sided geometrical shape. It is a polygon with five sides and five corners. A pentagon will be a regular pentagon if all of its sides are equal in length and all of its angles are equal. The image below is a regular pentagon with equal size of sides and angles:
A geometrical shape with five equal sizes of sides and equal size of angles.
A geometrical shape with five unequal sizes of sides and unequal size of angles.
If a pentagon has no internal angle greater than 180 degree, it is a convex pentagon.
If a pentagon has an internal angle greater than 180 degree, it is a concave pentagon.
Here are the formulas for various properties of pentagon:
Pentagon area can be calculated by using the below formula:
\(\text{A}=\dfrac{a^2}{4}\times\sqrt{\left(25+10\times \sqrt{5}\right)}\)
In this equation:
A refers to the area of the pentagon, and
a refers to the side of the pentagon.
\(\text{p} = 5 \times\text{a}\)
In this equation:
p refers to the perimeter of the pentagon, and
a refers to the side of the pentagon
Pentagon diagonal can be calculated by using the below formula:
\(\text{d}=\dfrac{a} {2}\times\left(1 + \sqrt{5}\right)\)
In this equation:
d refers to the diagonal of the pentagon,
a refers to the side of the pentagon
Pentagon height can be calculated by using the below formula:
\(\text{h}=\dfrac{a}{2}\times \sqrt{\left(5 + 2\times \sqrt{5}\right)}\)
In this equation:
h refers to the height of pentagon, and
a refers to the side of the pentagon
A regular pentagon has two types of radius, circumcircle radius and incircle radius.
Circumcircle radius of pentagon can be calculated by using the below formula:
\(r_i=\dfrac{a}{10}\times\sqrt{\left(50 + 10\times\sqrt{5}\right)}\)
In this equation:
r_{c} refers to the circumcircle radius of the pentagon, and
a refers to the side of the pentagon
Incircle radius of pentagon can be calculated by using the below formula:
\(r_c=\dfrac{a}{10}\times\sqrt{\left(25+10\times\sqrt{5}\right)}\)
In this equation:
r_{i} refers to the incircle radius of the pentagon, and
a refers to the side of the pentagon
Area of pentagon can be calculated by using the above formula for pentagon area. Follow these steps to calculate area of pentagon:
Let’s use an example to understand how to find the area of the pentagon. Suppose a regular pentagon has a side of \(6\) cm. Calculate the area of the pentagon.
Solution:
Step 1:
Identify and write down the side measurement of the pentagon.
\(\text{a} = 6 \text{cm}\)
Step 2:
Write down the pentagon area formula.
\(\text{A}=\dfrac{a^2}{4}\times \sqrt{\left(25+10\times \sqrt{5}\right)}\)
Step 3:
Substitute the values in the formula and calculate the area of the pentagon.
\(\text{A}=\dfrac{6^2}{4}\times \sqrt{\left(25+10\times \sqrt{5}\right)}\)
\(\text{A}=\dfrac{36}{4}\times \sqrt{\left(25+10\times \sqrt{5}\right)}\)
\(\text{A} = 61.94 cm^2\)
So, if a pentagon has a side of \(6\) cm, its area will be \(61.94 cm^2\) approximately.
Perimeter of pentagon can be calculated by using the above formula for pentagon perimeter. Follow these steps to calculate the perimeter of pentagon:
Example:
Let’s use the same example above to understand how to find the perimeter of the pentagon. Suppose a regular pentagon has a side of \(6\) cm. Calculate the perimeter of the pentagon.
Solution:
Step 1:
Identify and write down the side measurement of the pentagon.
\(\text{a} = 6 \text{cm}\)
Step 2:
Write down the pentagon perimeter formula.
\(\text{p} = 5 \times\text{a}\)
Step 3:
Substitute the values in the formula and calculate the perimeter of the pentagon.
\(\text{p} = 5 \times\text{a}\)
\(\text{p} = 5 \times 6\)
\(\text{p} = 30 \text{cm}\)
So, if a pentagon has a side of \(6\) cm, its perimeter will be \(30\) cm approximately. By using the above formulas, you can calculate the diagonal, height, incircle radius, and circumcircle radius of the pentagon in the same way we have calculated its area and perimeter. However, you can always use the above pentagon calculator to save time. You can also use our polygon calculator if you need to calculate the polygon area.
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