Property dimensions-convert to acres

[lholmes]

Can you tell me what my acreage is? My lot is somewhat pie-shaped

N 00 10 degrees E 286.61 feet
S 41 degrees 00 E 181.5 feet
N 26 degrees 17 E 165.47 feet
(Doesn't indicate) 48.55 feet

Thanks for your time.

[Guest]

Can you tell me what my acreage is? My lot is somewhat pie-shaped

N 00 10 degrees E 286.61 feet
S 41 degrees 00 E 181.5 feet
N 26 degrees 17 E 165.47 feet
(Doesn't indicate) 48.55 feet

Thanks for your time.

There are various ways to proceed. For me, the easiest way is to add a diagonal that divides it into two triangles.

The angle at the apex of 286.61' and 181.5' sides 41 degrees 10'. Then the length of the diagonal can be calculated by the law of cosines:
c^2 = a^2 + b^2 -2*a*b*cos C

Once c is found, all three sides of both triangles are known, and their areas may be found by Heron's formula. If a, b, c are the three sides, form:
s = 0.5*(a + b + c), then area K is given by
K = SQRT(s*(s-a)*(s-b)*(s-c))
Add the two triangles together

Solving, c = 191.747
For the first triangle, s = 329.9285,
K = 17121 sq ft.

for triangle two (same diagonal and other two sides),
s = 202.8835, K = 3611.95 sq ft.

Total area = 20,733 sq ft approx. 1 acre = 43560 sq ft, so 0.476 acre.