FormulaDen.com

Physics Chemistry Math Chemical Engineering Civil Electrical Electronics Electronics and Instrumentation Materials Science Mechanical Production Engineering Financial Health

Inradius of Pentagon given Diagonal Formula

GoInradius of Pentagon given Edge Length using Central Angle Formula

GoInradius of Pentagon given Circumradius using Central Angle Formula

Fx Copy

LaTeX Copy

The Inradius of Pentagon is defined as the radius of the circle which is inscribed inside the Pentagon. Check FAQs

r i = \sqrt{25 + (10 \cdot \sqrt{5})} \cdot \frac{d}{5 \cdot (1 + \sqrt{5})}

r_i - Inradius of Pentagon?d - Diagonal of Pentagon?

Inradius of Pentagon given Diagonal Example

With values

With units

Only example

Here is how the Inradius of Pentagon given Diagonal equation looks like with Values.

Here is how the Inradius of Pentagon given Diagonal equation looks like with Units.

Here is how the Inradius of Pentagon given Diagonal equation looks like.

6.8052 = \sqrt{25 + (10 \cdot \sqrt{5})} \cdot \frac{16}{5 \cdot (1 + \sqrt{5})}

6.8052m = \sqrt{25 + (10 \cdot \sqrt{5})} \cdot \frac{16m}{5 \cdot (1 + \sqrt{5})}

6.8052 = \sqrt{25 + (10 \cdot \sqrt{5})} \cdot \frac{16}{5 \cdot (1 + \sqrt{5})}

Tip: Use pencil ( Pencil

) icon above to edit Input Values and Units.

Calculate

Recalculate

Solution

Copy

Reset

You are here -

Home » Category

Math » Category

Geometry » Category

2D Geometry » fx Inradius of Pentagon given Diagonal

Inradius of Pentagon given Diagonal Solution

Follow our step by step solution on how to calculate Inradius of Pentagon given Diagonal?

FIRST Step Consider the formula

r i = \sqrt{25 + (10 \cdot \sqrt{5})} \cdot \frac{d}{5 \cdot (1 + \sqrt{5})}

Next Step Substitute values of Variables

∴

r i = \sqrt{25 + (10 \cdot \sqrt{5})} \cdot \frac{16m}{5 \cdot (1 + \sqrt{5})}

Next Step Prepare to Evaluate

∴

r i = \sqrt{25 + (10 \cdot \sqrt{5})} \cdot \frac{16}{5 \cdot (1 + \sqrt{5})}

Next Step Evaluate

∴

r i = 6.80520646681632m

LAST Step Rounding Answer

∴

r i = 6.8052m

Inradius of Pentagon given Diagonal Formula Elements

Variables

Functions

Inradius of Pentagon

The Inradius of Pentagon is defined as the radius of the circle which is inscribed inside the Pentagon.

Symbol: r_i

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Inradius of Pentagon

Diagonal of Pentagon

Diagonal of Pentagon is a straight line joining two non adjacent vertices of a Pentagon.

Symbol: d

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Diagonal of Pentagon

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other Formulas to find Inradius of Pentagon

Go Inradius of Pentagon given Edge Length using Central Angle

r i = \frac{l e}{2 \cdot \tan (\frac{π}{5})}

Go Inradius of Pentagon given Circumradius using Central Angle

r i = r c \cdot \cos (\frac{π}{5})

Go Inradius of Pentagon given Circumradius

r i = \frac{\sqrt{25 + (10 \cdot \sqrt{5})}}{\sqrt{50 + (10 \cdot \sqrt{5})}} \cdot r c

Go Inradius of Pentagon given Height using Central Angle

r i = \frac{h}{1 + (\frac{1}{\cos (\frac{π}{5})})}

How to Evaluate Inradius of Pentagon given Diagonal?

Inradius of Pentagon given Diagonal evaluator uses Inradius of Pentagon = sqrt(25+(10*sqrt(5)))*Diagonal of Pentagon/(5*(1+sqrt(5))) to evaluate the Inradius of Pentagon, The Inradius of Pentagon given Diagonal formula is defined as the length of the line joining the center and a point on the incircle of Pentagon, calculated using diagonal of Pentagon. Inradius of Pentagon is denoted by r_i symbol.

How to evaluate Inradius of Pentagon given Diagonal using this online evaluator? To use this online evaluator for Inradius of Pentagon given Diagonal, enter Diagonal of Pentagon (d) and hit the calculate button.

FAQs on Inradius of Pentagon given Diagonal

What is the formula to find Inradius of Pentagon given Diagonal?

The formula of Inradius of Pentagon given Diagonal is expressed as Inradius of Pentagon = sqrt(25+(10*sqrt(5)))*Diagonal of Pentagon/(5*(1+sqrt(5))). Here is an example- 6.805206 = sqrt(25+(10*sqrt(5)))*16/(5*(1+sqrt(5))).

How to calculate Inradius of Pentagon given Diagonal?

With Diagonal of Pentagon (d) we can find Inradius of Pentagon given Diagonal using the formula - Inradius of Pentagon = sqrt(25+(10*sqrt(5)))*Diagonal of Pentagon/(5*(1+sqrt(5))). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Inradius of Pentagon?

Here are the different ways to Calculate Inradius of Pentagon-

Inradius of Pentagon=(Edge Length of Pentagon)/(2*tan(pi/5))
Inradius of Pentagon=Circumradius of Pentagon*cos(pi/5)
Inradius of Pentagon=sqrt(25+(10*sqrt(5)))/sqrt(50+(10*sqrt(5)))*Circumradius of Pentagon

Can the Inradius of Pentagon given Diagonal be negative?

No, the Inradius of Pentagon given Diagonal, measured in Length cannot be negative.

Which unit is used to measure Inradius of Pentagon given Diagonal?

Inradius of Pentagon given Diagonal is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Inradius of Pentagon given Diagonal can be measured.

Let Others Know

✖

Facebook

Twitter

Copied!

: Value
: Unit