Have you ever dealt with the frustration of forgetting the equation to solve the area of a triangle?

The panic that ensues while you fumble around to find the piece of paper with your equation scribbled on it is pretty much unbearable. And it can be pretty embarrassing to ask someone else for the equation because you’ve lost or forgotten it, as well.

So how do you deal with this predicament? The good news is that it’s pretty easy to find an area of triangle calculator online, and they’re quite easy to use! 

Triangle basics

A triangle is a polygon with three sides, or vertices. A vertex is where two (or more) lines, edges or curves converge. With triangles, the line segments (which are called edges) are what make up the vertices. The “angles” of a triangle are its vertices. 

Typically the sides of the triangle are what you need to pay the most attention to when using an area of triangle calculator, so we’ll go into a bit more detail about those here than the actual vertices or angles. 

Marks on the sides of a triangle (called “tick marks”) are used to depict the length of that side. If two sides have the same number of tick marks on them, it’s an indication that they’re the same length.

There’s a similar system for the angles of a triangle, and if two angles have the same markings then they’re the same size, as well.

A triangle with three sides that are the same length is called an equilateral triangle. Your area of triangle calculator may show an equilateral triangle, but that doesn’t mean that it thinks the dimensions you’ve entered will create an equilateral triangle- it’s just a placeholder picture in most cases. 

Triangles can also be described based on their angles, and fall into one of two categories: right or oblique. If one of a triangle’s  angles is 90 degrees, then it’s a right triangle. The hypotenuse of a right angle is the longest side, which is to the right of the right angle. 

Any other triangle is an oblique triangle, and these consist of either acute or obtuse triangles. An acute triangle has angles less than 90 degrees, while obtuse triangles have at least one angle that’s more than 90 degrees. 

So, even if your area of triangle calculator shows an equilateral triangle, it could easily be an acute, obtuse or right triangle. 

It’s important when using an area of triangle calculator that a triangle can’t have more than one angle that’s 90 degrees or more. If it does, then whatever that shape is it isn’t a triangle. The sum of the exterior angles of a triangle add up to 360 degrees, while the sum of the interior angles adds up to 180 degrees. 

The Pythagorean Theorem was developed specifically for right triangles. This theory states that the hypotenuse squared will always be equal to the squared lengths of the other two sides added together.

There are oddball exceptions to this rule that can get quite complicated, but in general you can remember this theorem by memorizing the phrase “A squared plus B squared equals C squared”, and it typically looks a bit like this in execution: 

a² + b² = c²
EX: Given a = 3, c = 5, find b:
3² + b² = 5²
9 + b² = 25
b² = 16 => b = 4

Using the Law of Sines makes it possible to find out the unknown values of angles and sides of a triangle if you’ve got enough information to execute the proper calculation.

This law states that the length of one side of a triangle over to its sine of the opposite angle is a constant, which means that doesn’t change.

The sides of the triangle are typically described as a, b, and c, while the angles are designated as A, B, and C. This probably sounds pretty complicated, and it can be. Here’s a graphic to depict this calculation. 

It’s worth noting that there are exceptions to this, as well. 

If you know the values of the sides of a triangle, you can determine the values of its angles using this equation: 

Area of a triangle

Of course, this is the meat and potatoes section of our area of triangle calculator article. Of course, you can use an area of triangle calculator to determine the area of a triangle, but it’s also important to know how to find the area manually. 

To find the area of a triangle and effectively use an area of triangle calculator, you need to know some terms. First, the height of a triangle is the angle perpendicular to the base, drawn from the vertex to the opposite side.

The base is typically the bottom of the triangle and forms a right angle with the height. In this picture, the line between R and Q makes up the base. 

The most popular equation for finding the area of a triangle, and likely the one your area of triangle calculator will use, is as follows: area = 1/2 b * h. 

There’s another way to find the area of a triangle without an area of triangle calculator. Heron’s formula doesn’t require you to know the base or height of the triangle, but it does require you to know the length of all three of its sides. Here we’ll assume that a= 3, b= 4 and c= 5. 

Other triangle metrics you should know

Depending on the type of area of triangle calculator you use, it may ask for some of these metrics, so they’re useful to know. 

Median

The median of a triangle is the length of a line that goes from the vertex to the midpoint of the opposite side.

Triangles can have three separate medians that meet at the centroid, which is the center of the triangle where the medians meet. This illustration does a great job of depicting both the medians of a triangle and the centroid. 

_{The medians are ma, mb, and mc, and here’s how you can find the value of a median.} 

_{If a=2, b=3 and c= 4, you can find ma with this calculation:} 

Inradius

The inradius is an interesting measure of polygons that indicates the radius of the biggest circle that will fit inside a given polygon, in this case a triangle.

To find the inradius, find the incenter of one of the sides of the triangle and the inradius will be in the perpendicular distance between the incenter and the side. It doesn’t matter which side you use because the true center is an equal distance from all of the sides. Here’s what the inradius looks like: 

Typically an area of triangle calculator will use an equation that uses the area of the triangle and the semiparameter of the triangle as well as an equation similar to this to find the inradius: 

In this example, a, b, and c all represent the sides of the triangle. 

Circumradius

The last additional measurement you’ll want to know when using an area of triangle calculator is the circumradius. The circumradius is the radius of a circle that passes through all of the triangle’s vertices.

The circle’s center is also the circumcenter of the triangle where all of its bisectors from its sides meet. The triangle’s circumcenter doesn’t have to be inside the triangle. And all triangles have a circumcircle and circumradius. Here’s an example of what a circumradius may look like: 

And here’s an equation that your area of triangle calculator may use to find the circumradius of your triangle: 

In this equation, a is one side of the triangle and A is the angle opposite that side. You can use any side (a, b or c) and the angle opposite it to find the circumradius using this equation. 

Area of triangle calculator

It’s not terribly difficult to find an area of triangle calculator online, but finding one with all of the features you need may be difficult. 

This area of triangle calculator by Gigacalculator has several different options, including options to solve the area using side and height, the three sides, two sides and an included angle, two sides and a non-included angle, two angles and an included side, two angles and a non-included side, as well as an equation using the hypotenuse and leg.

It also includes information at the bottom of the page for many of these calculations so that you can memorize them and use them later when you don’t have access to a computer or phone to look the equations up. (Or if you’re in class and your teacher won’t allow you to use an area of triangle calculator!) 

This area of triangle calcularor by Squarefootagearea has many of the options that Gigacalculator offers, with the addition of equations for equilateral triangles and right triangles. 

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