Triangle Area Calculator

A triangle is a figure closed by three line segments. The line segments are known as sides Of the triangle. The area covered by the triangle is known as the triangle area. The Triangle area can be calculated in many ways. Here triangle area calculator is based on the height of the triangle and base length of the triangle.

Calculate the Triangle Area

Fill the Triangle Base and Height and Hit Calculate Button


Triangle Area Calculator
Height 0
Base 0
Area ( Height x base /2 ) 0

Triangle Area Calculation Formula

The formula of Area of Triangular region 

In the previous part, we learned that area of the triangular region = 1/2 * base * height. In the following part, we have added some other relevant formulas

Right-angled triangle

Let in the right-angled triangle ABC, BC = a, and AB = b are the adjacent sides of the right angle. Here if we consider BC as the base and AB as the height

Area of  ABC = 1/2 × base × height = 1/2 ab

Two sides of a triangular region and the angle included between them are given

Let in ABC, the sides are 

BC = a, CA = b, AB =c.

AD is drawn perpendicular from A to BC. Let altitude (height) AD = h.

Considering the angle C we get, AD / CA = sinC

or, h/b = sinC or, h = bsinC

Area of ABC = 1/2 × BC × AD

Area of ABC = 1/2 × BC × AD

= 1/2 a × b sinC = 1/2 × absinC

Similarly, area of ABC = 1/2 bcsinA =1/2 casinB


Three sides of a triangle are given
Let in ABC, BC = a, CA = b and AB = c.

Perimeter of the triangle 2s = a + b + c.

We draw AD ⊥ BC.

Let, BD = x, then CD = a − x

In right-angled ABD and ACD

AD² = AB² − BD² and AD² = AC² − CD²

AB² − BD² =AC² − CD²

or, c² − x² = b² − (a − x)²

or, c² − x² = b² − a² + 2ax − x²

or, 2ax = c² + a² − b²

x = c² + a² − b²/ 2a

Again, 

AD²  = c² − x² 

AD²  = c² − (c² + a² − b²/ 2a)² 

AD²  = (c + c² + a² − b²/ 2a) (c - c² + a² − b²/ 2a)

AD²  = (2ac + c² + a² − b²/ 2a) (2ac - c² + a² − b²/ 2a)

AD²  = {(c + a)²  − b² } {b²  − (c − a)² }/4a² 

AD²  = (a + b + c) (a + b + c − 2b) (a+ b + c − 2a) (a+ b + c − 2c)/ 4a² 

AD²  =  2s(2s − 2b)(2s − 2a)(2s − 2c)/4a² 

AD²  =4s(s − a)(s − b)(s − c)/a²

AD = 2/a √s(s − a)(s − b)(s − c)

 

Area of ABC = 1/2 BC × AD

 =1/2 x a x 2/a  √{s(s − a)(s − b)(s − c)}

 =√{s(s − a)(s − b)(s − c)}

Equilateral triangle

Equilateral triangle: Let the length of each side of the equilateral triangular region ABC be a.

Draw AD ⊥ BC.

BD = CD = a/2

In right-angled ABD

BD² + AD² = AB²

or, AD² = AB² − BD² = a² − (a/2)²

or, AD² = a² − a²/4

or, AD² =4a² − a²/4

AD = √3a/2

Area of ABC = 1/2 BC × AD

=  1/2 × a × √3a/2=√3/4 a²

 

Isosceles triangle

Let ABC be an isosceles triangle in which

AB = AC = a and BC = b

Draw, AD is perpendicular BC. BD = CD = b/2

ABD is right angled.

AD² = AB² − BD²

AD²  = a² − (b/2)²

AD²  = a² − b²/4

AD²  = (4a² − b²)/4

AD = √(4a² − b²)/2

Area of isosceles  ABC = 1/2 BC × AD
 = 1/2 × b × √(4a² − b²)/2
 = b/4 √(4a² − b²)