**Problem Statement **

Theres a 10x10 barn. At one corner of the barn there is a rope attached to it that extends 100ft long. Find the area that the cow can graze.

**Process **

**Solution **

We first started by finding the area of each of these shapes. Heres what we did:

Area of 3/4 of the circle is:

Area of Triangles:

Area of Sectors:

Now the final and last step is to add all the areas that we solved for up together.

**3/4 of Circle**- Used the formula πr^2 to find the area of the whole circle.
**π100^2 = 31,400** - Because we need only 3/4 of the circle we multiple it by
**3/4 or .75 so 31,400 x .75 = 23,550**

Area of 3/4 of the circle is:

**23,550**

__Triangles__- Inorder to find area of the broken up triangles we need to figure out the base and height by using the Pythagorean theorem. Finding the base: 10^2 + 10^2 = c^2.....
**C= 14.14 (Base)**. Knowing our base we were able to use the same formula to find the height. h^2 + 7.07 = 90^2.......**H= 89.7 (Height)** ****Thanks to pythagorean theorem we were able to use our base and height that we found to plug it into our formula to find the area of the triangles.**( 14.14/89.7) ÷ 2 = 634.2**- With the 634.2 we had to subtract it by 5o because of the area the cuts into the barn.
**634.2 - 50 = 584.2**

Area of Triangles:

**584.2****Sectors**- Used inverse trig to find the missing angle that we need for our sector. We used S^-1 = o/h .
**Sin^-1 89/90 = 85,3°** - Because we were given the 45° angle and we just solved for 85.3° this is all we needed to find our piece for our sector.
**180 - (45° + 85.3°) = 49.7°**- With out given angle we divide that by 360 so that we could find the percentage of that part of the circle.
**49.7 ÷ 360 = .138** - The 13.8 will be the number your use to multiply after finding the area of the circle with the dip. This radius is the one with 90 because of the wanky corner that took of 10ft. So that means
**π90^2 = 25,434** - With our area we could now multiply it with the percentage of the sector that we actually need.
**25,434 (.138) = 3,509.9** - We aren't done yet! We need to multiply 3,509.9 x 2 because we have two sectors. So
**3,509.9 x 2 = 7019.7**

Area of Sectors:

**7019.7****Final Step**Now the final and last step is to add all the areas that we solved for up together.

**23,550 + 584.2 + 7019.7 = Total area of which the cow can graze**

Total Area that the cow can graze : 31,154Total Area that the cow can graze : 31,154

**Reflection**

If I were to grade myself during this cow problem I would give myself an A+ because of the growth that I had with this problem. At first it was really complicated for me to even understand the problem and I only got as far as creating the first digram but, because I was curious, and because I had a growth mindset I asked a lot of question to my group members and was engaged in the problem the whole time. Once I understood the problem completely and got to the actual math solving part I felt very confident because it started to look familiar. Personally what pushed my thinking was when it was my group mates asking me questions. This pushed me to ask myself why and to try and explain in a way that would make sense to them. I realized that maybe the way I learned it and the way I had it explained to me didn't make as much sense to someone else so I was challenged to explain why we were doing each step and how.