Area of Triangle of Lune Calculator

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✖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.ⓘ Radius of Smaller Circle of Lune [r_Smaller]			+10% -10%
✖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.ⓘ Radius of Larger Circle of Lune [r_Larger]			+10% -10%
✖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.ⓘ Distance of Centers of Circles of Lune [d_Centers]			+10% -10%

✖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.ⓘ Area of Triangle of Lune [A_Triangle]

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Formula

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Area of Triangle of Lune

Formula

`"A"_{"Triangle"} = sqrt(("r"_{"Smaller"}+"r"_{"Larger"}+"d"_{"Centers"})*("r"_{"Larger"}+"d"_{"Centers"}-"r"_{"Smaller"})*("d"_{"Centers"}+"r"_{"Smaller"}-"r"_{"Larger"})*("r"_{"Smaller"}+"r"_{"Larger"}-"d"_{"Centers"}))/4`

Example

`"19.81004m²"=sqrt(("5m"+"8m"+"10m")*("8m"+"10m"-"5m")*("10m"+"5m"-"8m")*("5m"+"8m"-"10m"))/4`

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Area of Triangle of Lune Solution

STEP 0: Pre-Calculation Summary

Formula Used

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
A_Triangle = sqrt((r_Smaller+r_Larger+d_Centers)*(r_Larger+d_Centers-r_Smaller)*(d_Centers+r_Smaller-r_Larger)*(r_Smaller+r_Larger-d_Centers))/4
This formula uses 1 Functions, 4 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 of Lune - (Measured in Square Meter) - 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.
Radius of Smaller Circle of Lune - (Measured in Meter) - 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.
Radius of Larger Circle of Lune - (Measured in Meter) - 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.
Distance of Centers of Circles of Lune - (Measured in Meter) - 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.

STEP 1: Convert Input(s) to Base Unit

Radius of Smaller Circle of Lune: 5 Meter --> 5 Meter No Conversion Required
Radius of Larger Circle of Lune: 8 Meter --> 8 Meter No Conversion Required
Distance of Centers of Circles of Lune: 10 Meter --> 10 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

A_Triangle = sqrt((r_Smaller+r_Larger+d_Centers)*(r_Larger+d_Centers-r_Smaller)*(d_Centers+r_Smaller-r_Larger)*(r_Smaller+r_Larger-d_Centers))/4 --> sqrt((5+8+10)*(8+10-5)*(10+5-8)*(5+8-10))/4

Evaluating ... ...

A_Triangle = 19.8100353356575

STEP 3: Convert Result to Output's Unit

19.8100353356575 Square Meter --> No Conversion Required

FINAL ANSWER

19.8100353356575 ≈ 19.81004 Square Meter <-- Area of Triangle of Lune

(Calculation completed in 00.004 seconds)

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Home » Math » Geometry » 2D Geometry » Lune » Area of Triangle of Lune

Credits

Created by Jaseem K

IIT Madras (IIT Madras), Chennai

Jaseem K has created this Calculator and 100+ more calculators!

Verified by Nikita Kumari

The National Institute of Engineering (NIE), Mysuru

Nikita Kumari has verified this Calculator and 600+ more calculators!

< 4 Lune Calculators

Area of Large Lune

Go Area of Large Lune = (pi*(Radius of Larger Circle of Lune^2-Radius of Smaller Circle of Lune^2))+(2*Area of Triangle of Lune)+(Radius of Smaller Circle of Lune^2*arccos((Radius of Larger Circle of Lune^2-Radius of Smaller Circle of Lune^2-Distance of Centers of Circles of Lune^2)/(2*Radius of Smaller Circle of Lune*Distance of Centers of Circles of Lune)))-(Radius of Larger Circle of Lune^2*arccos((Radius of Larger Circle of Lune^2+Distance of Centers of Circles of Lune^2-Radius of Smaller Circle of Lune^2)/(2*Radius of Larger Circle of Lune*Distance of Centers of Circles of Lune)))

Area of Section of Lune

Go Area of Section of Lune = (pi*Radius of Smaller Circle of Lune^2)-((2*Area of Triangle of Lune)+(Radius of Smaller Circle of Lune^2*arccos((Radius of Larger Circle of Lune^2-Radius of Smaller Circle of Lune^2-Distance of Centers of Circles of Lune^2)/(2*Radius of Smaller Circle of Lune*Distance of Centers of Circles of Lune)))-(Radius of Larger Circle of Lune^2*arccos((Radius of Larger Circle of Lune^2+Distance of Centers of Circles of Lune^2-Radius of Smaller Circle of Lune^2)/(2*Radius of Larger Circle of Lune*Distance of Centers of Circles of Lune))))

Area of Small Lune

Go Area of Small Lune = (2*Area of Triangle of Lune)+(Radius of Smaller Circle of Lune^2*arccos((Radius of Larger Circle of Lune^2-Radius of Smaller Circle of Lune^2-Distance of Centers of Circles of Lune^2)/(2*Radius of Smaller Circle of Lune*Distance of Centers of Circles of Lune)))-(Radius of Larger Circle of Lune^2*arccos((Radius of Larger Circle of Lune^2+Distance of Centers of Circles of Lune^2-Radius of Smaller Circle of Lune^2)/(2*Radius of Larger Circle of Lune*Distance of Centers of Circles of Lune)))

Area of Triangle of Lune

Go 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

Area of Triangle of Lune Formula

What is a Lune?

When two circle intersects each other, and remove the intersection part. The shape thus obtained is called a Lune. The Latin word 'luna' means 'moon'. The shape Lune is actually a combination of two crescent moon shapes joined each other and facing oppositely.

How to Calculate Area of Triangle of Lune?

Area of Triangle of Lune calculator 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 calculate 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 calculate Area of Triangle of Lune using this online calculator? To use this online calculator 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. Here is how the Area of Triangle of Lune calculation can be explained with given input values -> 19.81004 = sqrt((5+8+10)*(8+10-5)*(10+5-8)*(5+8-10))/4.

FAQ

What is 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 and is represented as A_Triangle = sqrt((r_Smaller+r_Larger+d_Centers)*(r_Larger+d_Centers-r_Smaller)*(d_Centers+r_Smaller-r_Larger)*(r_Smaller+r_Larger-d_Centers))/4 or 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. 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, 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 & 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.

How to calculate 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 is calculated using 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 calculate Area of Triangle of Lune, you need 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). With our tool, you need to enter the respective value for Radius of Smaller Circle of Lune, Radius of Larger Circle of Lune & Distance of Centers of Circles of Lune and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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