Inradius of Equilateral Triangle given Area Calculator

✖The Area of Equilateral Triangle is the amount of space or region occupied by the Equilateral triangle in the plane.ⓘ Area of Equilateral Triangle [A]

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✖The Inradius of Equilateral Triangle is defined as the radius of the circle which is inscribed inside the triangle.ⓘ Inradius of Equilateral Triangle given Area [r_i]

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Formula

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Inradius of Equilateral Triangle given Area

Formula

`"r"_{"i"} = sqrt(("A")/(3*sqrt(3)))`

Example

`"2.402811m"=sqrt(("30m²")/(3*sqrt(3)))`

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Inradius of Equilateral Triangle given Area Solution

STEP 0: Pre-Calculation Summary

Formula Used

Inradius of Equilateral Triangle = sqrt((Area of Equilateral Triangle)/(3*sqrt(3)))
r_i = sqrt((A)/(3*sqrt(3)))
This formula uses 1 Functions, 2 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

Inradius of Equilateral Triangle - (Measured in Meter) - The Inradius of Equilateral Triangle is defined as the radius of the circle which is inscribed inside the triangle.
Area of Equilateral Triangle - (Measured in Square Meter) - The Area of Equilateral Triangle is the amount of space or region occupied by the Equilateral triangle in the plane.

STEP 1: Convert Input(s) to Base Unit

Area of Equilateral Triangle: 30 Square Meter --> 30 Square Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_i = sqrt((A)/(3*sqrt(3))) --> sqrt((30)/(3*sqrt(3)))

Evaluating ... ...

r_i = 2.40281141413475

STEP 3: Convert Result to Output's Unit

2.40281141413475 Meter --> No Conversion Required

FINAL ANSWER

2.40281141413475 ≈ 2.402811 Meter <-- Inradius of Equilateral Triangle

(Calculation completed in 00.020 seconds)

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Home » Math » Geometry » 2D Geometry » Triangle » Equilateral Triangle » Radius of Equilateral Triangle » Inradius of Equilateral Triangle » Inradius of Equilateral Triangle given Area

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Osmania University (OU), Hyderabad

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< 9 Inradius of Equilateral Triangle Calculators

Inradius of Equilateral Triangle given Area

Go Inradius of Equilateral Triangle = sqrt((Area of Equilateral Triangle)/(3*sqrt(3)))

Inradius of Equilateral Triangle given Semiperimeter

Go Inradius of Equilateral Triangle = Semiperimeter of Equilateral Triangle/(3*sqrt(3))

Inradius of Equilateral Triangle

Go Inradius of Equilateral Triangle = Edge Length of Equilateral Triangle/(2*sqrt(3))

Inradius of Equilateral Triangle given Perimeter

Go Inradius of Equilateral Triangle = Perimeter of Equilateral Triangle/(6*sqrt(3))

Inradius of Equilateral Triangle given Length of Angle Bisector

Go Inradius of Equilateral Triangle = 1/3*Length of Angle Bisector of Equilateral Triangle

Inradius of Equilateral Triangle given Circumradius

Go Inradius of Equilateral Triangle = 1/2*Circumradius of Equilateral Triangle

Inradius of Equilateral Triangle given Exradius

Go Inradius of Equilateral Triangle = 1/3*Exradius of Equilateral Triangle

Inradius of Equilateral Triangle given Median

Go Inradius of Equilateral Triangle = 1/3*Median of Equilateral Triangle

Inradius of Equilateral Triangle given Height

Go Inradius of Equilateral Triangle = Height of Equilateral Triangle/3

Inradius of Equilateral Triangle given Area Formula

Inradius of Equilateral Triangle = sqrt((Area of Equilateral Triangle)/(3*sqrt(3)))
r_i = sqrt((A)/(3*sqrt(3)))

What is Equilateral Triangle?

In geometry, an Equilateral Triangle is a triangle in which all three sides have the same length. In the familiar Euclidean geometry, an equilateral triangle is also equiangular; that is, all three internal angles are also congruent to each other and are each 60°.

How to Calculate Inradius of Equilateral Triangle given Area?

Inradius of Equilateral Triangle given Area calculator uses Inradius of Equilateral Triangle = sqrt((Area of Equilateral Triangle)/(3*sqrt(3))) to calculate the Inradius of Equilateral Triangle, The Inradius of Equilateral Triangle given Area formula is defined as the length of the radius of the largest circle contained in the triangle and touches (is tangent to) all the three sides of equilateral triangle, calculated using area. Inradius of Equilateral Triangle is denoted by r_i symbol.

How to calculate Inradius of Equilateral Triangle given Area using this online calculator? To use this online calculator for Inradius of Equilateral Triangle given Area, enter Area of Equilateral Triangle (A) and hit the calculate button. Here is how the Inradius of Equilateral Triangle given Area calculation can be explained with given input values -> 2.402811 = sqrt((30)/(3*sqrt(3))).

FAQ

What is Inradius of Equilateral Triangle given Area?

The Inradius of Equilateral Triangle given Area formula is defined as the length of the radius of the largest circle contained in the triangle and touches (is tangent to) all the three sides of equilateral triangle, calculated using area and is represented as r_i = sqrt((A)/(3*sqrt(3))) or Inradius of Equilateral Triangle = sqrt((Area of Equilateral Triangle)/(3*sqrt(3))). The Area of Equilateral Triangle is the amount of space or region occupied by the Equilateral triangle in the plane.

How to calculate Inradius of Equilateral Triangle given Area?

The Inradius of Equilateral Triangle given Area formula is defined as the length of the radius of the largest circle contained in the triangle and touches (is tangent to) all the three sides of equilateral triangle, calculated using area is calculated using Inradius of Equilateral Triangle = sqrt((Area of Equilateral Triangle)/(3*sqrt(3))). To calculate Inradius of Equilateral Triangle given Area, you need Area of Equilateral Triangle (A). With our tool, you need to enter the respective value for Area of Equilateral 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 Inradius of Equilateral Triangle?

In this formula, Inradius of Equilateral Triangle uses Area of Equilateral Triangle. We can use 8 other way(s) to calculate the same, which is/are as follows -

Inradius of Equilateral Triangle = Edge Length of Equilateral Triangle/(2*sqrt(3))
Inradius of Equilateral Triangle = Height of Equilateral Triangle/3
Inradius of Equilateral Triangle = Perimeter of Equilateral Triangle/(6*sqrt(3))
Inradius of Equilateral Triangle = 1/2*Circumradius of Equilateral Triangle
Inradius of Equilateral Triangle = 1/3*Exradius of Equilateral Triangle
Inradius of Equilateral Triangle = 1/3*Median of Equilateral Triangle
Inradius of Equilateral Triangle = Semiperimeter of Equilateral Triangle/(3*sqrt(3))
Inradius of Equilateral Triangle = 1/3*Length of Angle Bisector of Equilateral Triangle

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