Area of Triangle given Three Exradii and Inradius Calculator

✖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.ⓘ Exradius Opposite to ∠A of Triangle [r_e(∠A)]			+10% -10%
✖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.ⓘ Exradius Opposite to ∠B of Triangle [r_e(∠B)]			+10% -10%
✖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.ⓘ Exradius Opposite to ∠C of Triangle [r_e(∠C)]			+10% -10%
✖Inradius of Triangle is defined as the radius of the circle which is inscribed inside the Triangle.ⓘ Inradius of Triangle [r_i]			+10% -10%

✖The Area of Triangle is the amount of region or space occupied by the Triangle.ⓘ Area of Triangle given Three Exradii and Inradius [A]

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Area of Triangle given Three Exradii and Inradius Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
A = sqrt(r_e(∠A)*r_e(∠B)*r_e(∠C)*r_i)
This formula uses 1 Functions, 5 Variables

Functions Used

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., sqrt(Number)

Variables Used

Area of Triangle - (Measured in Square Meter) - The Area of Triangle is the amount of region or space occupied by the Triangle.
Exradius Opposite to ∠A of Triangle - (Measured in Meter) - 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.
Exradius Opposite to ∠B of Triangle - (Measured in Meter) - 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.
Exradius Opposite to ∠C of Triangle - (Measured in Meter) - 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.
Inradius of Triangle - (Measured in Meter) - Inradius of Triangle is defined as the radius of the circle which is inscribed inside the Triangle.

STEP 1: Convert Input(s) to Base Unit

Exradius Opposite to ∠A of Triangle: 5 Meter --> 5 Meter No Conversion Required
Exradius Opposite to ∠B of Triangle: 8 Meter --> 8 Meter No Conversion Required
Exradius Opposite to ∠C of Triangle: 32 Meter --> 32 Meter No Conversion Required
Inradius of Triangle: 3 Meter --> 3 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

A = sqrt(r_e(∠A)*r_e(∠B)*r_e(∠C)*r_i) --> sqrt(5*8*32*3)

Evaluating ... ...

A = 61.9677335393187

STEP 3: Convert Result to Output's Unit

61.9677335393187 Square Meter --> No Conversion Required

FINAL ANSWER

61.9677335393187 ≈ 61.96773 Square Meter <-- Area of Triangle

(Calculation completed in 00.015 seconds)

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Created by Venkata Sai Prasanna Aradhyula

Birla Institute of Technology & Science (BITS), Hyderabad

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< Area of Triangle Calculators

Area of Triangle

LaTeX Go 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

Area of Triangle by Heron's Formula

LaTeX Go 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 given Two Angles and Third Side

LaTeX Go Area of Triangle = (Side A of Triangle^2*sin(Angle B of Triangle)*sin(Angle C of Triangle))/(2*sin(pi-Angle B of Triangle-Angle C of Triangle))

Area of Triangle given Base and Height

LaTeX Go Area of Triangle = 1/2*Side C of Triangle*Height on Side C of Triangle

Area of Triangle given Three Exradii and Inradius Formula

LaTeX Go

What is a Triangle ?

A Triangle is a type of polygon, which have three sides and three vertices. This is a two-dimensional figure with three straight sides. A triangle is considered a 3-sided polygon. The sum of all the three angles of a triangle is equal to 180°. The triangle is contained in a single plane. Based on its sides and angle measurement, the triangle has six types.

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

Area of Triangle given Three Exradii and Inradius calculator 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 calculate 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 calculate Area of Triangle given Three Exradii and Inradius using this online calculator? To use this online calculator 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. Here is how the Area of Triangle given Three Exradii and Inradius calculation can be explained with given input values -> 61.96773 = sqrt(5*8*32*3).

FAQ

What is Area of Triangle given Three Exradii and Inradius?

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 and is represented as A = sqrt(r_e(∠A)*r_e(∠B)*r_e(∠C)*r_i) or 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). 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, 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, 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 & Inradius of Triangle is defined as the radius of the circle which is inscribed inside the Triangle.

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

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 is calculated using 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 calculate Area of Triangle given Three Exradii and Inradius, you need 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). With our tool, you need to enter the respective value for Exradius Opposite to ∠A of Triangle, Exradius Opposite to ∠B of Triangle, Exradius Opposite to ∠C of Triangle & Inradius of Triangle and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Area of Triangle?

In this formula, Area of Triangle uses Exradius Opposite to ∠A of Triangle, Exradius Opposite to ∠B of Triangle, Exradius Opposite to ∠C of Triangle & Inradius of Triangle. We can use 3 other way(s) to calculate the same, which is/are as follows -

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

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