Area of Triangle 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%

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

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Formula

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Area of Triangle

Formula

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

Example

`"64.99231m²"=sqrt(("10m"+"14m"+"20m")*("14m"+"20m"-"10m")*("10m"-"14m"+"20m")*("10m"+"14m"-"20m"))/4`

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Area of Triangle Solution

STEP 0: Pre-Calculation Summary

Formula Used

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
A = sqrt((S_a+S_b+S_c)*(S_b+S_c-S_a)*(S_a-S_b+S_c)*(S_a+S_b-S_c))/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 - (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.

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

STEP 2: Evaluate Formula

Substituting Input Values in Formula

A = sqrt((S_a+S_b+S_c)*(S_b+S_c-S_a)*(S_a-S_b+S_c)*(S_a+S_b-S_c))/4 --> sqrt((10+14+20)*(14+20-10)*(10-14+20)*(10+14-20))/4

Evaluating ... ...

A = 64.9923072370877

STEP 3: Convert Result to Output's Unit

64.9923072370877 Square Meter --> No Conversion Required

FINAL ANSWER

64.9923072370877 ≈ 64.99231 Square Meter <-- Area of Triangle

(Calculation completed in 00.004 seconds)

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Credits

Created by Venkata Sai Prasanna Aradhyula

Birla Institute of Technology & Science (BITS), Hyderabad

Venkata Sai Prasanna Aradhyula has created this Calculator and 10+ more calculators!

Verified by Anamika Mittal

Vellore Institute of Technology (VIT), Bhopal

Anamika Mittal has verified this Calculator and 300+ more calculators!

< 9 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 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 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

< 6 Area of Triangle Calculators

Area of Triangle

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 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 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 Formula

What is 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.

How to Calculate Area of Triangle?

Area of Triangle calculator uses 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 to calculate the Area of Triangle, Area of Triangle is defined as the total region that is enclosed by a particular triangle. Area of Triangle is denoted by A symbol.

How to calculate Area of Triangle using this online calculator? To use this online calculator for Area of Triangle, enter Side A of Triangle (S_a), Side B of Triangle (S_b) & Side C of Triangle (S_c) and hit the calculate button. Here is how the Area of Triangle calculation can be explained with given input values -> 64.99231 = sqrt((10+14+20)*(14+20-10)*(10-14+20)*(10+14-20))/4.

FAQ

What is Area of Triangle?

Area of Triangle is defined as the total region that is enclosed by a particular triangle and is represented as A = sqrt((S_a+S_b+S_c)*(S_b+S_c-S_a)*(S_a-S_b+S_c)*(S_a+S_b-S_c))/4 or 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. 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.

How to calculate Area of Triangle?

Area of Triangle is defined as the total region that is enclosed by a particular triangle is calculated using 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. To calculate Area of Triangle, you need Side A of Triangle (S_a), Side B of Triangle (S_b) & Side C of Triangle (S_c). With our tool, you need to enter the respective value for Side A of Triangle, Side B of Triangle & Side C 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. We can use 13 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 = (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 = (Side A of Triangle*Side B of Triangle*Side C of Triangle)/(4*Circumradius of Triangle)
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 = Inradius of Triangle*Semiperimeter of Triangle
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 = 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

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