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Area of Triangle Formula

GoArea of Triangle given Inradius and Semiperimeter Formula

GoArea of Triangle given Two Angles and Third Side Formula

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The Area of Triangle is the amount of region or space occupied by the Triangle. Check FAQs

A = \frac{\sqrt{(S a + S b + S c) \cdot (S b + S c - S a) \cdot (S a - S b + S c) \cdot (S a + S b - S c)}}{4}

A - Area of Triangle?S_a - Side A of Triangle?S_b - Side B of Triangle?S_c - Side C of Triangle?

Area of Triangle Example

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

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

Here is how the Area of Triangle equation looks like.

64.9923 = \frac{\sqrt{(10 + 14 + 20) \cdot (14 + 20 - 10) \cdot (10 - 14 + 20) \cdot (10 + 14 - 20)}}{4}

64.9923m² = \frac{\sqrt{(10m + 14m + 20m) \cdot (14m + 20m - 10m) \cdot (10m - 14m + 20m) \cdot (10m + 14m - 20m)}}{4}

64.9923 = \frac{\sqrt{(10 + 14 + 20) \cdot (14 + 20 - 10) \cdot (10 - 14 + 20) \cdot (10 + 14 - 20)}}{4}

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Area of Triangle Solution

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

FIRST Step Consider the formula

A = \frac{\sqrt{(S a + S b + S c) \cdot (S b + S c - S a) \cdot (S a - S b + S c) \cdot (S a + S b - S c)}}{4}

Next Step Substitute values of Variables

∴

A = \frac{\sqrt{(10m + 14m + 20m) \cdot (14m + 20m - 10m) \cdot (10m - 14m + 20m) \cdot (10m + 14m - 20m)}}{4}

Next Step Prepare to Evaluate

∴

A = \frac{\sqrt{(10 + 14 + 20) \cdot (14 + 20 - 10) \cdot (10 - 14 + 20) \cdot (10 + 14 - 20)}}{4}

Next Step Evaluate

∴

A = 64.9923072370877m²

LAST Step Rounding Answer

∴

A = 64.9923m²

Area of Triangle Formula Elements

Variables

Functions

Area of Triangle

The Area of Triangle is the amount of region or space occupied by the Triangle.

Symbol: A

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Area of Triangle

Side A 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.

Symbol: S_a

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Side A of Triangle

Side B of Triangle

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.

Symbol: S_b

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Side B of Triangle

Side C of Triangle

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.

Symbol: S_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Side C of Triangle

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 to find Area of Triangle

Go Area of Triangle given Inradius and Semiperimeter

A = r i \cdot s

Go Area of Triangle given Two Angles and Third Side

A = \frac{{S a}^{2} \cdot \sin (∠B) \cdot \sin (∠C)}{2 \cdot \sin (π - ∠B - ∠C)}

Go Area of Triangle given Two Sides and Third Angle

A = S a \cdot S b \cdot \frac{\sin (∠C)}{2}

Go Area of Triangle by Heron's Formula

A = \sqrt{s \cdot (s - S a) \cdot (s - S b) \cdot (s - S c)}

How to Evaluate Area of Triangle?

Area of Triangle evaluator 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 evaluate 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 evaluate Area of Triangle using this online evaluator? To use this online evaluator 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.

FAQs on Area of Triangle

What is the formula to find Area of Triangle?

The formula of Area of Triangle is expressed as 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. Here is an example- 64.99231 = sqrt((10+14+20)*(14+20-10)*(10-14+20)*(10+14-20))/4.

How to calculate Area of Triangle?

With Side A of Triangle (S_a), Side B of Triangle (S_b) & Side C of Triangle (S_c) we can find Area of Triangle using the formula - 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. This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Area of Triangle?

Here are the different ways to Calculate Area 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

Can the Area of Triangle be negative?

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

Which unit is used to measure Area of Triangle?

Area of Triangle 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 can be measured.

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: Value
: Unit

Area of Triangle Formula

​GoArea of Triangle given Inradius and Semiperimeter Formula

​GoArea of Triangle given Two Angles and Third Side Formula

Area of Triangle Example

Area of Triangle Solution

Area of Triangle Formula Elements

Other Formulas to find Area of Triangle

How to Evaluate Area of Triangle?

FAQs on Area of Triangle

Variable Name

GoArea of Triangle given Inradius and Semiperimeter Formula

GoArea of Triangle given Two Angles and Third Side Formula