Can someone explain the formula for the area of a pentagon, and the formula for the length of an arc of a portion of a circle? .

So a pentagon is constructed by five identical triangles, that's why you can find the area of one triangle and multiply it with 5:
A_pentagon=A_triangle*5
To find the area of a triangle you must use tangens.
You can watch this for more on that on youtube. 

For the length of an arc or a portion of a circle you can find it using: 
arc lenght = 2π*r(A/360), where A=angle. 
So if you know radians, then 2π is a whole circle. And to calculate for the specific circle you have to use the radius. That's why you multiply with radius, which is the only difference between any two different circles. you then multiply with the  part of the circle that you want to find the lenght for, which is A/360 (because there are 360° in a circle)

I hope that helped.