Heronian triangle

A Heronian triangle is a special kind of triangle where all the sides and the area are whole numbers. Imagine you have a pizza and you want to cut it into three equal pieces. If you want each piece to have a whole number of slices, you may need to experiment until you figure out how many slices will work. That’s kind of like what happens with a Heronian triangle.

When you draw a triangle, you can measure each side with a ruler. The length of each side is a number, and if all three numbers are whole numbers, you have a Heronian triangle. But it’s not just enough for the sides to be whole numbers, the area of the triangle needs to be a whole number too.

Let's try to make a Heronian triangle. We can use sticks of different lengths to make a triangle. If we use sticks that are 6 inches, 8 inches, and 10 inches long, we can create a triangle with the sticks. The lengths of the sides are whole numbers, so this is a Heronian triangle.

Now, how do we find out if the area of a triangle is a whole number? To do that, we need to calculate the area. The formula for finding the area of a triangle is base times height divided by 2.

We can measure a base and height using a ruler too. If the base and height we measure also turn out to be whole numbers then the area of the triangle will be a whole number. We can also use a bit of math to work out the area even if we don’t have a ruler handy. So, if the sides of your triangle and the area can all be whole numbers, then you have a Heronian triangle!