# The Area Of My Land In Florida

## Piece of Land

These are the actual measurements of the perimeter of the piece of land that I am convincing my Realtor the correct area of. I found 5 of the 6 angles by myself with a protractor. I am finding the hypotenuse on my own and using law of sine and law of cosine to make sure of amount of land being measured.

## Steps to Prove My Correctness

In proving that I am correct, I found some of the sides and angles using law of sine and law of cosine. Following that, I found the area of my two separated triangles that are inside my trapezoid of land.

The law of sine states a/sin(A)=b/sin(B), a/sin(A)=c/sin(C), b/sin(B)=c/sin(C).

The law of cosine states that a^2=b^2+c^2-2(c)(b)cos(A),b^2=a^2+c^2-2(a)(c)cos(B),c^2=b^2+a^2-2(a)(b)cos(C)

## Law of Sine

To use law of sine, I split my trapezoid into two triangles. For the first triangle I found side c, and for the second triangle I found side a.

Side C=2311.68 feet, which is very close to the original measurement.

Side A=3271.41 feet, which is also very close to the original measurement.

## Law of Cosine

To use the law of cosine, I split my trapezoid into two triangle. For the first triangle I found side b, and for the second triangle I found and B.

Side B=3854.29 feet. This is correct because it is the hypotenuse of the firs triangle and a normal side of the second triangle. The hypotenuse is the longest side in a triangle, and that is what it is for triangle one making it accurate.

Angle B=61 degrees. This seems accurate because in the piece of land which side c and side a meet forms a acute angle. An acute angle is less than 90 degrees and this angle is less than 90 degrees.

## Finding the Area

To find the area I used the formula 1/2(a)(b)sin(C). I had to find the area of each triangle and then add them together.

The area all together became 8,313,810 ft squared. Although this seem like a lot, it is very accurate for this huge piece of land. The side are almost a mile long, so the square footage seems accurate.