Area of a triangle

There are a few different ways to calculate the area of a triangle. This is important for three reasons:

1. In any situation, one of the ways will be easiest. But which way is easiest depends on the situation. So it’s good to know many ways, so that you’ll always have an easy way.
2. If you can calculate the area of a triangle in two different ways, then you have a way to check your work (since the area of a triangle should be the same no matter how you get there).
3. If you can calculate the area of a triangle in two different ways, and you remember that the area must work out to be the same no matter which method you use, then you can calculate the area in one way, then use that area as the answer to a different method, to allow you to figure out something you otherwise wouldn’t be able to. For example, if you know that the area of a triangle is bh/2, and you know that a particular triangle has an area of 15 and a base of 6, then you can work out that its height must be 5.

Here are some different ways to calculate the area of a triangle:

• The easiest way to calculate the area of a triangle is to multiply its base by its height and then divide the result by two. In other words, area = (base) * (height) / 2, or A=bh/2.
• Another way to find the area of a triangle is to think of a different side as the base and use the same technique. Some people prefer to think of this as rotating the triangle so that a different side is at the bottom.
• Another way is to draw a rectangle around the triangle, calculate the area of the rectangle, then subtract out the parts that are inside the rectangle but outside the triangle. This works especially well when the triangle is on the coordinate plane.
• There’s also a thing called Heron’s formula. It’s complicated, but it works in a lot of situations where nothing else does. The formula is $A=\sqrt{s\ast (s-a)\ast (s-b)\ast (s-c)}$. Let me translate that to plain English: if you have a triangle whose side lengths are a, b, and c, then start by adding up the three sides and dividing by two. This is called the semiperimeter (because it’s half the perimeter) and we label it s. Then you multiply the four terms s, s-a, s-b, and s-c together, then take the square root of the result. What you have left is the area of the triangle.
• Finally, there are also some ways that require trigonometry, but we won’t get into that right now.