# I don't get the second parts of mini explanation. What does s equal to for it to be used in there at the end?

• Module 2 Week 4 Day 16 Challenge Part 2

I dont get the second parts of mini explanation. What does s equal to for it to be used in there at the end?

• @The-Darkin-Blade Hi again! The variable $$s$$ is there just to make the expression look a little bit cleaner and to make Heron's Formula easier to memorize. See, $$s$$ is just half of the triangle's perimeter, or the semiperimeter:

$$s = \frac{ a + b + c}{2}$$

If we tried to remember Heron's Formula only in terms of $$a, b,$$ and $$c,$$ (without $$s$$), the expression would look a lot more ugly. It would look like this:

$$\sqrt{(\frac{a + b + c}{2} )(\frac{-a + b + c}{2} )(\frac{a - b + c}{2} )(\frac{a + b -c }{2}}$$

There's another nice thing about $$s$$: since it is equal to the perimeter divided by $$2,$$ it takes us a long way toward the area formula for a triangle.

Remember the area formula is

$$\frac{1}{2} \times \text{ base } \times \text{ height}$$

So all you have to do to get the area of the triangle is take $$s$$ and multiply it to the sum of the heights of each triangle!