Python has hundreds and hundreds of functions. Most are not immediately available as built ins. Instead, the functions are saved into different modules, and you need to tell Python that you'd like to use them. Similarly, your own functions may also be saved into different modules. We will demonstrate this using our triangle triangle.pie example. We will define a second function to calculate the area of the triangle, for when you know the lengths of the three sides but not the base and height. This time, we'll calculate the area of the triangle using Heron's formula, also known as Heroes formula. The formula involves both the semi perimeter and the lengths of the three sides. S is the semi perimeter, s1, s2 and s3 are the lengths of the three sides of the triangle. In order to write this code, we need to calculate the semi perimeter. And we already have a function to do this, defined in triangle.pi. And we also need a function to calculate the square root, and such a function exists, but it isn't a built-in function. Instead, it is defined in another file named math.pi. Math is a module, as is triangle. As its name implies, the math module contains several functions related to math. To see the listing of functions, let's import the module to gain access to it. And then we'll call the built-in function dir r. We see that a function named square root is amongst the available functions, and we can now run help and square root to find out more about it. When we ask for information about square root, we need to specify that it is in the Math module. We do that using the module name, followed by a dot, followed by the function name. And this tells us information about the square root function. Now, we're ready to write the function. The first step is going to be to write a couple of example function calls. And in order to do that, we need to decide on a meaningful function name. I'll use the word area along with hero to indicate that we're using hero's formula. This function takes three sides, and in this case, I would expect it to return 6.0. We'll add a second function call, second example. And in this case, using my calculator, I've figured out, you should be getting back something like thi 27.731. There will be a few more digits, and I don't know exactly what, because Python uses floating point arithmetic. But this will give me a sense of whether the function that we're writing is correct or not. Now, we'll provide the type contract for this function. We'll pass in three numbers, either ints or floats, and it will return a float. We're ready now to add the function header. Beginning with the word def and the function name. Along with the three parameters, which I'm going to name side1, side2, and side3. And at this stage, we can add the description. This function will return to the area for the triangle with sides of length, side 1, side 2 and side 3. With the [INAUDIBLE] string complete, we can now work on the body of the function. The formula uses the semi-perimeter four different times. And rather than call the semi-perimeter four different times with the same arguments. We can call it once and store the results in a variable. I'll name that variable semi, and then we'll call semi-perimeter once to calculate it, with side1, side2, and side 3 as arguments. Then we can move on to calculating the area. When we calculate the area, we'll use the square root function and square root is in the Math module. So to access square root, we need to import the Math module. I'll do that at the top of my file. And then I will be able to gain access to the square root function. [UNKNOWN] Calculate the area. We'll call square root from that using the model name, dot, and the function name, and we'll pass in the following. Semi times semi minus side1 time semi minus side2 times semi minus side3. And that area is what this function will return. Finally, we need to test the function by calling it a couple of times. So, I'm going to re-size this window, and run the module. Then we'll just re-size this, and will copy and paste these function calls. So the first function call should result in 6.0 and it does. And the second example should give us something like what we had there, and in fact it's giving us more digits. I'm going to use that result here instead. So that's what we expect to get. It's not only Python's modules that we can import. We can also import a module that we wrote. For example, if we wanted to use one of our triangle functions in another module, we could import triangle. The module being imported should be in the same directory as the module that's importing it.
