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Area of Triangle of Lune Formula

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The Area of Triangle of Lune is the total quantity of plane occupied by the triangle joining the centers of two circles of Lune and one of their intersecting point. Check FAQs

A Triangle = \frac{\sqrt{(r Smaller + r Larger + d Centers) \cdot (r Larger + d Centers - r Smaller) \cdot (d Centers + r Smaller - r Larger) \cdot (r Smaller + r Larger - d Centers)}}{4}

A_Triangle - Area of Triangle of Lune?r_Smaller - Radius of Smaller Circle of Lune?r_Larger - Radius of Larger Circle of Lune?d_Centers - Distance of Centers of Circles of Lune?

Area of Triangle of Lune Example

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Here is how the Area of Triangle of Lune equation looks like with Values.

Here is how the Area of Triangle of Lune equation looks like with Units.

Here is how the Area of Triangle of Lune equation looks like.

19.81 = \frac{\sqrt{(5 + 8 + 10) \cdot (8 + 10 - 5) \cdot (10 + 5 - 8) \cdot (5 + 8 - 10)}}{4}

19.81m² = \frac{\sqrt{(5m + 8m + 10m) \cdot (8m + 10m - 5m) \cdot (10m + 5m - 8m) \cdot (5m + 8m - 10m)}}{4}

19.81 = \frac{\sqrt{(5 + 8 + 10) \cdot (8 + 10 - 5) \cdot (10 + 5 - 8) \cdot (5 + 8 - 10)}}{4}

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Area of Triangle of Lune Solution

Follow our step by step solution on how to calculate Area of Triangle of Lune?

FIRST Step Consider the formula

A Triangle = \frac{\sqrt{(r Smaller + r Larger + d Centers) \cdot (r Larger + d Centers - r Smaller) \cdot (d Centers + r Smaller - r Larger) \cdot (r Smaller + r Larger - d Centers)}}{4}

Next Step Substitute values of Variables

∴

A Triangle = \frac{\sqrt{(5m + 8m + 10m) \cdot (8m + 10m - 5m) \cdot (10m + 5m - 8m) \cdot (5m + 8m - 10m)}}{4}

Next Step Prepare to Evaluate

∴

A Triangle = \frac{\sqrt{(5 + 8 + 10) \cdot (8 + 10 - 5) \cdot (10 + 5 - 8) \cdot (5 + 8 - 10)}}{4}

Next Step Evaluate

∴

A Triangle = 19.8100353356575m²

LAST Step Rounding Answer

∴

A Triangle = 19.81m²

Area of Triangle of Lune Formula Elements

Variables

Functions

Area of Triangle of Lune

The Area of Triangle of Lune is the total quantity of plane occupied by the triangle joining the centers of two circles of Lune and one of their intersecting point.

Symbol: A_Triangle

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Area of Triangle of Lune

Radius of Smaller Circle of Lune

The Radius of Smaller Circle of Lune is the radius of the circle with lesser size, out of the two circles using which the Lune is created.

Symbol: r_Smaller

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Radius of Smaller Circle of Lune

Radius of Larger Circle of Lune

The Radius of Larger Circle of Lune is the radius of the circle with greater size, out of the two circles using which the Lune is created.

Symbol: r_Larger

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Radius of Larger Circle of Lune

Distance of Centers of Circles of Lune

The Distance of Centers of Circles of Lune is the length of the line joining the centers of two circles with which the Lune is created.

Symbol: d_Centers

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Distance of Centers of Circles of Lune

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 in Lune category

Go Area of Small Lune

A Small = (2 \cdot A Triangle) + ({r Smaller}^{2} \cdot \arccos (\frac{{r Larger}^{2} - {r Smaller}^{2} - {d Centers}^{2}}{2 \cdot r Smaller \cdot d Centers})) - ({r Larger}^{2} \cdot \arccos (\frac{{r Larger}^{2} + {d Centers}^{2} - {r Smaller}^{2}}{2 \cdot r Larger \cdot d Centers}))

Go Area of Large Lune

A Large = (π \cdot ({r Larger}^{2} - {r Smaller}^{2})) + (2 \cdot A Triangle) + ({r Smaller}^{2} \cdot \arccos (\frac{{r Larger}^{2} - {r Smaller}^{2} - {d Centers}^{2}}{2 \cdot r Smaller \cdot d Centers})) - ({r Larger}^{2} \cdot \arccos (\frac{{r Larger}^{2} + {d Centers}^{2} - {r Smaller}^{2}}{2 \cdot r Larger \cdot d Centers}))

Go Area of Section of Lune

A Section = (π \cdot {r Smaller}^{2}) - ((2 \cdot A Triangle) + ({r Smaller}^{2} \cdot \arccos (\frac{{r Larger}^{2} - {r Smaller}^{2} - {d Centers}^{2}}{2 \cdot r Smaller \cdot d Centers})) - ({r Larger}^{2} \cdot \arccos (\frac{{r Larger}^{2} + {d Centers}^{2} - {r Smaller}^{2}}{2 \cdot r Larger \cdot d Centers})))

How to Evaluate Area of Triangle of Lune?

Area of Triangle of Lune evaluator uses Area of Triangle of Lune = sqrt((Radius of Smaller Circle of Lune+Radius of Larger Circle of Lune+Distance of Centers of Circles of Lune)*(Radius of Larger Circle of Lune+Distance of Centers of Circles of Lune-Radius of Smaller Circle of Lune)*(Distance of Centers of Circles of Lune+Radius of Smaller Circle of Lune-Radius of Larger Circle of Lune)*(Radius of Smaller Circle of Lune+Radius of Larger Circle of Lune-Distance of Centers of Circles of Lune))/4 to evaluate the Area of Triangle of Lune, The Area of Triangle of Lune formula is defined as the quantity of plane enclosed by the triangle joined by the two centers of circles of Lune and any one of intersecting points of those circle. Area of Triangle of Lune is denoted by A_Triangle symbol.

How to evaluate Area of Triangle of Lune using this online evaluator? To use this online evaluator for Area of Triangle of Lune, enter Radius of Smaller Circle of Lune (r_Smaller), Radius of Larger Circle of Lune (r_Larger) & Distance of Centers of Circles of Lune (d_Centers) and hit the calculate button.

FAQs on Area of Triangle of Lune

What is the formula to find Area of Triangle of Lune?

The formula of Area of Triangle of Lune is expressed as Area of Triangle of Lune = sqrt((Radius of Smaller Circle of Lune+Radius of Larger Circle of Lune+Distance of Centers of Circles of Lune)*(Radius of Larger Circle of Lune+Distance of Centers of Circles of Lune-Radius of Smaller Circle of Lune)*(Distance of Centers of Circles of Lune+Radius of Smaller Circle of Lune-Radius of Larger Circle of Lune)*(Radius of Smaller Circle of Lune+Radius of Larger Circle of Lune-Distance of Centers of Circles of Lune))/4. Here is an example- 19.81004 = sqrt((5+8+10)*(8+10-5)*(10+5-8)*(5+8-10))/4.

How to calculate Area of Triangle of Lune?

With Radius of Smaller Circle of Lune (r_Smaller), Radius of Larger Circle of Lune (r_Larger) & Distance of Centers of Circles of Lune (d_Centers) we can find Area of Triangle of Lune using the formula - Area of Triangle of Lune = sqrt((Radius of Smaller Circle of Lune+Radius of Larger Circle of Lune+Distance of Centers of Circles of Lune)*(Radius of Larger Circle of Lune+Distance of Centers of Circles of Lune-Radius of Smaller Circle of Lune)*(Distance of Centers of Circles of Lune+Radius of Smaller Circle of Lune-Radius of Larger Circle of Lune)*(Radius of Smaller Circle of Lune+Radius of Larger Circle of Lune-Distance of Centers of Circles of Lune))/4. This formula also uses Square Root (sqrt) function(s).

Can the Area of Triangle of Lune be negative?

No, the Area of Triangle of Lune, measured in Area cannot be negative.

Which unit is used to measure Area of Triangle of Lune?

Area of Triangle of Lune 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 of Lune can be measured.

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Area of Triangle of Lune Formula

Area of Triangle of Lune Example

Area of Triangle of Lune Solution

Area of Triangle of Lune Formula Elements

Other formulas in Lune category

How to Evaluate Area of Triangle of Lune?

FAQs on Area of Triangle of Lune

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