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Tools City

Triangle Area Calculator

The whole space filled by a triangle's three sides in a two-dimensional plane is defined as its area. The area of a triangle varies depending on the length of the sides and its interior angles. The formula you will use for calculating the area of a triangle is: Area of a triangle = 1/2 × Base × Height.

base and height
Base and height triangle image
cm
cm
cm²

How can I use this tool?

You can use Tools City's Triangle Area Calculator free tool to calculate the desired triangle's area. You can use this free tool by selecting the desired triangle from the 'Given' dialogue box. After that, you can quickly enter the values in the available boxes displayed on the tool; instantly, the results will be displayed.

  • millimeters (mm)

  • centimeters (cm)

  • meters (m)

  • kilometers (km)

  • inch (in)

  • feet (ft)

  • yards (yd)

What Is the Area of a Triangle?

The whole space filled by a triangle's three sides in a two-dimensional plane is defined as its area.

The area of a triangle varies depending on the length of the sides and its interior angles.

The formula you will use for calculating the area of a triangle is

Area of a triangle = 1/2 × base × height.

This formula is implemented on all triangles, whether scalene, isosceles, or equilateral. It is already in your mind that a triangle's base and height are perpendicular to one another.

The area is calculated in square units, such as meter square, centimeter square, etc.

For Example

If the base of a triangle is 8 cm and the height of the triangle is 12 cm then its area will be:-

Area of a triangle = 1/2 × base × height.

A = 1/2 × 8 × 12 ≈ 48 cm2

The above method is the basic way of finding the area of a triangle; however, other options are also available on the tool, as mentioned below. We have provided the formulas and examples for these options so that you can do your requisite calculation by yourself.

  • three sides (SSS)
  • two sides + angle between (SAS)
  • two angles + side between (ASA)

How to find the area of a triangle with three sides (SSS)?

The Heron's Formula is used to calculate the area of a triangle having three sides. That formula is one of the best and easiest formulas developed by Heron of Alexandria, a Greek mathematician, and is still utilized. 

Area = √[s(s-a)(s-b)(s-c)]

In this formula, "s" represents the triangle's semi-perimeter, i.e., s = a + b + c / 2

For example:

Let us now take a look at an example to clearly understand the working of this formula

Let us consider: -

A = 3, B = 5, & C = 6

So, to calculate the area of a triangle, we first have to calculate the perimeter of the triangle,

Putting above values into the formula of perimeter:

S = A+B+C/2 = 3+5+6/2 ≈ 7

Now, putting the value of perimeter into the Heron’s Formula,

Area = √[s(s-a)(s-b)(s-c)]

Area = √[7(7-3)(7-5)(7-6)]

Area = √[7(4)(2)(1)]

Area = √[7(8)] = √[56] ≈ 7.48

What is the Area of Triangle With two Sides + angle between (SAS)?

When the two sides are given along with one angle of a triangle.

We will then apply the formulas:

  • When ‘A’ is angle and 'b' & 'c' are side:

Area (∆ABC) = 1/2 × bc × sin(A)

  • When ‘B’ is angle and 'a' & 'c' are sides:

Area (∆ABC) = 1/2 × ac × sin(B)

  • When ‘C’ is angle and 'a' & 'b' are sides:

Area (∆ABC) = 1/2 × ab × sin(C)

If you still feel any difficulty while solving it, then don’t worry; the below example will clear all the confusion you have in your mind.

For Example: 

If side A = 30°, and side 'b' = 8 units, side 'c' = 10 units.

Then, by using the formula given,

Area (∆ABC) = 1/2 × bc × sin A

= 1/2 × 8 × 10 × sin 30º

= 1/2 × 80 (0.5) ≈ 20

What is the Area of the Triangle With two angles + side between (ASA)?

When we are given two angles and a side in between

Area = a² × sin(β) × sin(γ) / (2 × sin(β + γ))

For Example

If we have two angles which are β = 45º and γ = 55º, and the side a = 10.

To find the area for this example, we will choose the formula with the a2 in it.

Area = a² × sin(β) × sin(γ) / (2 × sin(β + γ))

A = (10)2 × sin(45º× sin(55º) / 2 × sin (45º +55º)

A = 100 × 0.7071 × 0.8191 / (2 (0.9848) ≈ 29.41