FormulaDen.com

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

Area of Triangle given Three Exradii and Inradius Formula

GoArea of Triangle by Heron's Formula Formula

GoArea of Triangle given Base and Height Formula

Fx Copy

LaTeX Copy

The Area of Triangle is the amount of region or space occupied by the Triangle. Check FAQs

A = \sqrt{r e(∠A) \cdot r e(∠B) \cdot r e(∠C) \cdot r i}

A - Area of Triangle?r_e(∠A) - Exradius Opposite to ∠A of Triangle?r_e(∠B) - Exradius Opposite to ∠B of Triangle?r_e(∠C) - Exradius Opposite to ∠C of Triangle?r_i - Inradius of Triangle?

Area of Triangle given Three Exradii and Inradius Example

With values

With units

Only example

Here is how the Area of Triangle given Three Exradii and Inradius equation looks like with Values.

Here is how the Area of Triangle given Three Exradii and Inradius equation looks like with Units.

Here is how the Area of Triangle given Three Exradii and Inradius equation looks like.

61.9677 = \sqrt{5 \cdot 8 \cdot 32 \cdot 3}

61.9677m² = \sqrt{5m \cdot 8m \cdot 32m \cdot 3m}

61.9677 = \sqrt{5 \cdot 8 \cdot 32 \cdot 3}

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 Area of Triangle given Three Exradii and Inradius

Area of Triangle given Three Exradii and Inradius Solution

Follow our step by step solution on how to calculate Area of Triangle given Three Exradii and Inradius?

FIRST Step Consider the formula

A = \sqrt{r e(∠A) \cdot r e(∠B) \cdot r e(∠C) \cdot r i}

Next Step Substitute values of Variables

∴

A = \sqrt{5m \cdot 8m \cdot 32m \cdot 3m}

Next Step Prepare to Evaluate

∴

A = \sqrt{5 \cdot 8 \cdot 32 \cdot 3}

Next Step Evaluate

∴

A = 61.9677335393187m²

LAST Step Rounding Answer

∴

A = 61.9677m²

Area of Triangle given Three Exradii and Inradius Formula Elements

Variables

Functions

Area of Triangle

The Area of Triangle is the amount of region or space occupied by the Triangle.

Symbol: A

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Area of Triangle

Exradius Opposite to ∠A of Triangle

The Exradius Opposite to ∠A of triangle is the radius of circle formed with center as point of intersection of internal angle bisector of ∠A and external angle bisectors of other two angles.

Symbol: r_e(∠A)

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Exradius Opposite to ∠A of Triangle

Exradius Opposite to ∠B of Triangle

Exradius Opposite to ∠B of triangle is the radius of circle formed with center as point of intersection of internal angle bisector of ∠B and external angle bisectors of other two angles.

Symbol: r_e(∠B)

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Exradius Opposite to ∠B of Triangle

Exradius Opposite to ∠C of Triangle

Exradius Opposite to ∠C of triangle is the radius of circle formed with center as point of intersection of internal angle bisector of ∠C and external angle bisectors of other two angles.

Symbol: r_e(∠C)

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Exradius Opposite to ∠C of Triangle

Inradius of Triangle

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

Symbol: r_i

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Inradius of Triangle

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 Area of Triangle

Go Area of Triangle by Heron's Formula

A = \sqrt{s \cdot (s - S a) \cdot (s - S b) \cdot (s - S c)}

Go Area of Triangle given Base and Height

A = \frac{1}{2} \cdot S c \cdot h c

Go Area of Triangle

A = \frac{\sqrt{(S a + S b + S c) \cdot (S b + S c - S a) \cdot (S a - S b + S c) \cdot (S a + S b - S c)}}{4}

Go Area of Triangle given Two Angles and Third Side

A = \frac{{S a}^{2} \cdot \sin (∠B) \cdot \sin (∠C)}{2 \cdot \sin (π - ∠B - ∠C)}

How to Evaluate Area of Triangle given Three Exradii and Inradius?

Area of Triangle given Three Exradii and Inradius evaluator uses Area of Triangle = sqrt(Exradius Opposite to ∠A of Triangle*Exradius Opposite to ∠B of Triangle*Exradius Opposite to ∠C of Triangle*Inradius of Triangle) to evaluate the Area of Triangle, The Area of Triangle given Three Exradii and Inradius formula is defined as the total region enclosed inside the triangle, calculated using its exradii and inradius. Area of Triangle is denoted by A symbol.

How to evaluate Area of Triangle given Three Exradii and Inradius using this online evaluator? To use this online evaluator for Area of Triangle given Three Exradii and Inradius, enter Exradius Opposite to ∠A of Triangle (r_e(∠A)), Exradius Opposite to ∠B of Triangle (r_e(∠B)), Exradius Opposite to ∠C of Triangle (r_e(∠C)) & Inradius of Triangle (r_i) and hit the calculate button.

FAQs on Area of Triangle given Three Exradii and Inradius

What is the formula to find Area of Triangle given Three Exradii and Inradius?

The formula of Area of Triangle given Three Exradii and Inradius is expressed as Area of Triangle = sqrt(Exradius Opposite to ∠A of Triangle*Exradius Opposite to ∠B of Triangle*Exradius Opposite to ∠C of Triangle*Inradius of Triangle). Here is an example- 61.96773 = sqrt(5*8*32*3).

How to calculate Area of Triangle given Three Exradii and Inradius?

With Exradius Opposite to ∠A of Triangle (r_e(∠A)), Exradius Opposite to ∠B of Triangle (r_e(∠B)), Exradius Opposite to ∠C of Triangle (r_e(∠C)) & Inradius of Triangle (r_i) we can find Area of Triangle given Three Exradii and Inradius using the formula - Area of Triangle = sqrt(Exradius Opposite to ∠A of Triangle*Exradius Opposite to ∠B of Triangle*Exradius Opposite to ∠C of Triangle*Inradius of Triangle). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Area of Triangle?

Here are the different ways to Calculate Area of Triangle-

Area of Triangle=sqrt(Semiperimeter of Triangle*(Semiperimeter of Triangle-Side A of Triangle)*(Semiperimeter of Triangle-Side B of Triangle)*(Semiperimeter of Triangle-Side C of Triangle))
Area of Triangle=1/2*Side C of Triangle*Height on Side C of Triangle
Area of Triangle=sqrt((Side A of Triangle+Side B of Triangle+Side C of Triangle)*(Side B of Triangle+Side C of Triangle-Side A of Triangle)*(Side A of Triangle-Side B of Triangle+Side C of Triangle)*(Side A of Triangle+Side B of Triangle-Side C of Triangle))/4

Can the Area of Triangle given Three Exradii and Inradius be negative?

No, the Area of Triangle given Three Exradii and Inradius, measured in Area cannot be negative.

Which unit is used to measure Area of Triangle given Three Exradii and Inradius?

Area of Triangle given Three Exradii and Inradius is usually measured using the Square Meter[m²] for Area. Square Kilometer[m²], Square Centimeter[m²], Square Millimeter[m²] are the few other units in which Area of Triangle given Three Exradii and Inradius can be measured.

Let Others Know

✖

Facebook

Twitter

Copied!

: Value
: Unit

Area of Triangle given Three Exradii and Inradius Formula

​GoArea of Triangle by Heron's Formula Formula

​GoArea of Triangle given Base and Height Formula

Area of Triangle given Three Exradii and Inradius Example

Area of Triangle given Three Exradii and Inradius Solution

Area of Triangle given Three Exradii and Inradius Formula Elements

Other Formulas to find Area of Triangle

How to Evaluate Area of Triangle given Three Exradii and Inradius?

FAQs on Area of Triangle given Three Exradii and Inradius

Variable Name

GoArea of Triangle by Heron's Formula Formula

GoArea of Triangle given Base and Height Formula