Area of Triangle given Circumradius and Sides Calculator

✖The Side A of Triangle is the length of the side A, of the three sides of the triangle. In other words, the side A of the Triangle is the side opposite to the angle A.ⓘ Side A of Triangle [S_a]			+10% -10%
✖The Side B of Triangle is the length of the side B of the three sides. In other words, the side Bof the Triangle is the side opposite to the angle B.ⓘ Side B of Triangle [S_b]			+10% -10%
✖The Side C of Triangle is the length of the side C of the three sides. In other words, side C of the Triangle is the side opposite to angle C.ⓘ Side C of Triangle [S_c]			+10% -10%
✖Circumradius of Triangle is the radius of a circumcircle touching each of the vertices of the Triangle.ⓘ Circumradius of Triangle [r_c]			+10% -10%

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

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Formula

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Area of Triangle given Circumradius and Sides

Formula

`"A" = ("S"_{"a"}*"S"_{"b"}*"S"_{"c"})/(4*"r"_{"c"})`

Example

`"63.63636m²"=("10m"*"14m"*"20m")/(4*"11m")`

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Area of Triangle given Circumradius and Sides Solution

STEP 0: Pre-Calculation Summary

Formula Used

Area of Triangle = (Side A of Triangle*Side B of Triangle*Side C of Triangle)/(4*Circumradius of Triangle)
A = (S_a*S_b*S_c)/(4*r_c)
This formula uses 5 Variables

Variables Used

Area of Triangle - (Measured in Square Meter) - The Area of Triangle is the amount of region or space occupied by the Triangle.
Side A of Triangle - (Measured in Meter) - The Side A of Triangle is the length of the side A, of the three sides of the triangle. In other words, the side A of the Triangle is the side opposite to the angle A.
Side B of Triangle - (Measured in Meter) - The Side B of Triangle is the length of the side B of the three sides. In other words, the side Bof the Triangle is the side opposite to the angle B.
Side C of Triangle - (Measured in Meter) - The Side C of Triangle is the length of the side C of the three sides. In other words, side C of the Triangle is the side opposite to angle C.
Circumradius of Triangle - (Measured in Meter) - Circumradius of Triangle is the radius of a circumcircle touching each of the vertices of the Triangle.

STEP 1: Convert Input(s) to Base Unit

Side A of Triangle: 10 Meter --> 10 Meter No Conversion Required
Side B of Triangle: 14 Meter --> 14 Meter No Conversion Required
Side C of Triangle: 20 Meter --> 20 Meter No Conversion Required
Circumradius of Triangle: 11 Meter --> 11 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

A = (S_a*S_b*S_c)/(4*r_c) --> (10*14*20)/(4*11)

Evaluating ... ...

A = 63.6363636363636

STEP 3: Convert Result to Output's Unit

63.6363636363636 Square Meter --> No Conversion Required

FINAL ANSWER

63.6363636363636 ≈ 63.63636 Square Meter <-- Area of Triangle

(Calculation completed in 00.004 seconds)

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Birla Institute of Technology & Science (BITS), Hyderabad

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< 17 Area of Triangle Calculators

Area of Triangle

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

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

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 Three Exradii and Inradius

Go 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)

Area of Triangle given Circumradius and Sides

Go Area of Triangle = (Side A of Triangle*Side B of Triangle*Side C of Triangle)/(4*Circumradius of Triangle)

Area of Triangle using Sides A and B and Cosec of Angle C

Go Area of Triangle = (Side A of Triangle*Side B of Triangle)/(2*cosec(Angle C of Triangle))

Area of Triangle using Sides B and C and Cosec of Angle A

Go Area of Triangle = (Side A of Triangle*Side B of Triangle)/(2*cosec(Angle C of Triangle))

Area of Triangle using Sides A and C and Cosec of Angle B

Go Area of Triangle = (Side A of Triangle*Side C of Triangle)/(2*cosec(Angle B of Triangle))

Area of Triangle given Sides B and C and Sine of Angle A

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

Area of Triangle given Sides A and C and Sine of Angle B

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

Area of Triangle given Two Sides and Third Angle

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

Area of Triangle given Semiperimeter, One Side and its Exradius

Go Area of Triangle = Exradius Opposite to ∠A of Triangle*(Semiperimeter of Triangle-Side A of Triangle)

Area of Triangle given Side A and Sine of All Three Angles

Go Area of Triangle = (Side A of Triangle^2*Sin B*Sin C)/(2*Sin A)

Area of Triangle given Side B and Sine of All Three Angles

Go Area of Triangle = (Side B of Triangle^2*Sin A*Sin C)/(2*Sin B)

Area of Triangle given Side C and Sine of All Three Angles

Go Area of Triangle = (Side C of Triangle^2*Sin A*Sin B)/(2*Sin C)

Area of Triangle given Base and Height

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

Area of Triangle given Inradius and Semiperimeter

Go Area of Triangle = Inradius of Triangle*Semiperimeter of Triangle

Area of Triangle given Circumradius and Sides Formula

Area of Triangle = (Side A of Triangle*Side B of Triangle*Side C of Triangle)/(4*Circumradius of Triangle)
A = (S_a*S_b*S_c)/(4*r_c)

What is a Triangle ?

The Triangle is the 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.

What is Circumradius?

Circumradius is the radius of the circumcircle, which always passes through all three vertices of a triangle. Its center is at the point where all the perpendicular bisectors of the triangle's sides meet. This center is called the circumcenter.

How to Calculate Area of Triangle given Circumradius and Sides?

Area of Triangle given Circumradius and Sides calculator uses Area of Triangle = (Side A of Triangle*Side B of Triangle*Side C of Triangle)/(4*Circumradius of Triangle) to calculate the Area of Triangle, The Area of Triangle given Circumradius and Sides formula is defined as the total region that is enclosed by the three sides of any particular triangle, calculated using its circumradius and sides. Area of Triangle is denoted by A symbol.

How to calculate Area of Triangle given Circumradius and Sides using this online calculator? To use this online calculator for Area of Triangle given Circumradius and Sides, enter Side A of Triangle (S_a), Side B of Triangle (S_b), Side C of Triangle (S_c) & Circumradius of Triangle (r_c) and hit the calculate button. Here is how the Area of Triangle given Circumradius and Sides calculation can be explained with given input values -> 63.63636 = (10*14*20)/(4*11).

FAQ

What is Area of Triangle given Circumradius and Sides?

The Area of Triangle given Circumradius and Sides formula is defined as the total region that is enclosed by the three sides of any particular triangle, calculated using its circumradius and sides and is represented as A = (S_a*S_b*S_c)/(4*r_c) or Area of Triangle = (Side A of Triangle*Side B of Triangle*Side C of Triangle)/(4*Circumradius of Triangle). The Side A of Triangle is the length of the side A, of the three sides of the triangle. In other words, the side A of the Triangle is the side opposite to the angle A, The Side B of Triangle is the length of the side B of the three sides. In other words, the side Bof the Triangle is the side opposite to the angle B, The Side C of Triangle is the length of the side C of the three sides. In other words, side C of the Triangle is the side opposite to angle C & Circumradius of Triangle is the radius of a circumcircle touching each of the vertices of the Triangle.

How to calculate Area of Triangle given Circumradius and Sides?

The Area of Triangle given Circumradius and Sides formula is defined as the total region that is enclosed by the three sides of any particular triangle, calculated using its circumradius and sides is calculated using Area of Triangle = (Side A of Triangle*Side B of Triangle*Side C of Triangle)/(4*Circumradius of Triangle). To calculate Area of Triangle given Circumradius and Sides, you need Side A of Triangle (S_a), Side B of Triangle (S_b), Side C of Triangle (S_c) & Circumradius of Triangle (r_c). With our tool, you need to enter the respective value for Side A of Triangle, Side B of Triangle, Side C of Triangle & Circumradius 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 Side A of Triangle, Side B of Triangle, Side C of Triangle & Circumradius of Triangle. We can use 19 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
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 = Side A of Triangle*Side B of Triangle*sin(Angle C of Triangle)/2
Area of Triangle = Inradius of Triangle*Semiperimeter of Triangle
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)
Area of Triangle = Exradius Opposite to ∠A of Triangle*(Semiperimeter of Triangle-Side A of Triangle)
Area of Triangle = (Side B of Triangle*Side C of Triangle)/2*(sin(Angle A of Triangle))
Area of Triangle = (Side A of Triangle*Side C of Triangle)/2*(sin(Angle B of Triangle))
Area of Triangle = (Side A of Triangle*Side B of Triangle)/(2*cosec(Angle C of Triangle))
Area of Triangle = (Side A of Triangle*Side B of Triangle)/(2*cosec(Angle C of Triangle))
Area of Triangle = (Side A of Triangle*Side C of Triangle)/(2*cosec(Angle B of Triangle))
Area of Triangle = (Side A of Triangle^2*Sin B*Sin C)/(2*Sin A)
Area of Triangle = (Side B of Triangle^2*Sin A*Sin C)/(2*Sin B)
Area of Triangle = (Side C of Triangle^2*Sin A*Sin B)/(2*Sin C)
Area of Triangle = (Side A of Triangle^2*Cosec A)/(2*Cosec B*Cosec C)
Area of Triangle = (Side B of Triangle^2*Cosec B)/(2*Cosec A*Cosec C)
Area of Triangle = (Side C of Triangle^2*Cosec C)/(2*Cosec A*Cosec B)

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