These measurements are the sides of my lot. I need to know the total area?
2006-07-31 08:35:34 · 6 answers · asked by Michael R 1 in Science & Mathematics ➔ Mathematics
The dimensions given are in order starting
from the left side and working clockwise. Where 176.92 and 62.81 meet there is a right angle. Where 222.76 and 52.78 meet there is another right angle. Where 52.78 and 144.95 meet there is a third right angle.
2006-08-01 01:08:37 · update #1
Without measuring any of the angles, this problem is impossible to solve. Do any of the sides run parallel or perpendicular at all? Are the dimensions you gave in order? If they are, then the measurements of any two consecutive angles would be enough information to find the area of your lot.
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Okay, with the added info, we can figure out this area. :-) I'll divide your lot into three triangles, find the area of each, then add them up.
The right triangle made up with legs 176.92 and 62.81 has an area of 5556.1726 square feet.
A = ½bh
A = 176.92 · 62.81 / 2
A = 5556.1726
The hypotenuse (needed to find the third triangle) is 187.74 feet.
d = √(176.92² + 62.81²)
d = √(31300.6864 + 3945.0961)
d = √35245.7825
d = 187.7386
The right triangle made up with legs 226.76 and 52.78 has an area of 5984.1964 square feet.
A = ½bh
A = 226.76 · 52.78 / 2
A = 5984.1964
The hypotenuse (needed to find the third triangle) is 187.74 feet.
d = √(226.76² + 52.78²)
d = √(51420.0976 + 2785.7284)
d = √54205.826
d = 232.8214
The third triangle (made up of sides 144.95, 187.74, and 232.82) has an area of 13596.6954 square feet.
A = √[s(s - a)(s - b)(s - c), where s is the semiperimeter of the triangle.
s = (144.95 + 187.74 + 232.82) / 2
s = 565.51 / 2
s = 282.775
A = √[(282.755)(282.755 - 144.95)(282.755 - 187.74)(282.755 - 232.82)]
A = √184870126.5
A = 13596.6954
The three triangles comprise your entire lot, so the sum of the areas is the area for which you're looking.
5556.1726 + 5984.1964 + 13596.6954 = 25137.0644
The area of your lot is 25137.0644 square feet, or 0.577 acres.
2006-07-31 10:06:50 · answer #1 · answered by Anonymous · 0⤊ 0⤋
measuring angles is difficult
so divide the pentagon into 3 different triangles by measuring all the corners from one point...
Then calculate the area of three different triangles.
to calculate the area with the given information is not possible... there could be many pentagon with the sides given above...
Guessing 8632111.949 using the formula A = Sqrt [S * (S-a) * (S-b) * (S-c) * (S-d) * (S-e)]
of course i cant verify the equation. and i dont know if it can be applied to pentagon...
2006-07-31 08:50:33 · answer #2 · answered by fireashes 4 · 0⤊ 0⤋
Without knowing the angles involved, there is no definite solution. You must provide angles as well as sides to calculate the area.
2006-07-31 08:38:30 · answer #3 · answered by aichip_mark2 3 · 0⤊ 0⤋
Break the area into triangles. If you draw diagonals between the corners, you can break the pentagon into triangles whose areas are fairly easy to figure out.
2006-07-31 08:39:12 · answer #4 · answered by Sappho 4 · 0⤊ 0⤋
Sounds like you need a calculator to finish your homework.
2006-07-31 08:42:06 · answer #5 · answered by EG345 4 · 0⤊ 0⤋
This problem has no definite solution.
2006-07-31 09:43:29 · answer #6 · answered by dutch_prof 4 · 0⤊ 0⤋