The Area Of My Land In Florida

Emily Cocchiola

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.