can any1 tell me the size of a lot thats 78x120x111x120 acres and what measurements mean please?

Question

I am searching for a lot and I found the one above thats in my price range where I want to live but I dont know how much acreage this is or what the dimensions mean? as stated above they are listed as 78x120x111x120 if anyone can help me I would really appreciate it......Thanks

Answer 1

The shape of the lot is a trapezoid with an area of 11,232.27 square feet.

The lot has two sides of equal length, each 120 feet long, and two parallel sides, one side is 78 feet long and the other side is 111 feet long.

The formula for the area of a trapezoid is one half the sum of the lengths of the two parallel sides times the height of the trapezoid.

One half the sum of the lengths of the two parallel sides is: 78 feet plus 111 feet divided by 2. That is equal to 94.5 feet.

Now we have to determine the height of the trapezoid..

To determine the height of the trapezoid, we make a right triangle of the end of the trapedoid.

To do that we see that the side that is 111 feet long is 33 feet longer than the other parallel side which is 78 feet.

The side that is 111 feet is therefore 16.5 feet longer than the 78 foot side on both the left and right sides.

If we drop a straight line from each end of the 78 foot side we create two right triangles one on the left side of the trapezoid and one on the right side of th trapezoid.

This creates two right triangles. each wih a base of 16.5 feet and a hypoteneuse of 120 feet.

We now need to determine the height of the trapezsoid.

If we label the base as letter "A" , the height of the triangle as letter "B" and the hypoteneuse as letter "C" we can use the formula for the area of a right triangle, that is A squared plus B squared equals C squared.

We know that the base "A" is 16.5 feet, so "A" squared is equal to 272.25.

We know that the hypoteneuse "C" is 120 feet so "C" squared is 14,400.

We need to find the value of B squared.

Since "A" Squared plus "B" squared equals "C" squared.

If we subtract "A" squared from "C" squared we will get the value of "B" squared.

That is: 14,000 minus 272,25 = 14,127.75.

We now know that "B" squared is equal to 14,127.75.

If we take the square root of that number we get:118.86 which is equal to the value of "B" and that is equal to the height of the triangle. That is also equal to the height of the trapezoid.

If we multiply the height (118,86) feet times one half the sum of the lengths of the parallel sides (94.5) the result is 11,232.27 square feet.

Note that the 120 foot sides are not parallel and that they cannot be parallel. Only the 78 foot side and the 111 fot sides are parallel.

You an check this easily by drawing the figure on graph paper in the order that the dimensions are given to you.

Start with the 78 foot dimension. Draw left to right 78 squares on the graph paper. Now use the next dimension 120 feet making a right angle 120 squares down, The next dimension, 111 make a right angle again and draw 111 squares. Now try to use the last dimension of 120 feet using 120 squares try to connect back up with the 78 foot line using only 120 squares on your graph paper. It will not work.

The only way that you can connect these dimensions in the order given to you is to put the 78 foot dimension parallel to the 111 foot dimension and centered over the 111 foot dimension. The second and fourth dimensions of 120 feet each connect forming an angle. The figure looks like a triangle with the top cut off of it. That is called a trapezoid.

The answer that the second responder gave you is the area of a rectangle 120 feet long and 111 feet high, which is not correct. This figure is not a rectangle.

The answer that the first responder gave you is the area of a trapezoid with parallel sides of 78 feet and 111 feet and a height of 120 feet, which is not correct because the 120 foot sides are not parallel so they cannot be equal to the height.

The technique that I used to find the height of the trapezoid is from high school geometry and is a technique that is often used to determine the area of lots which are trapezoidal in shape.

Answer 2

lot sizes are normally measured in feet & 100th of a foot then converted to acreage. The lot size you described is odd shaped. The tax assessors office would have the square footage calculation.

Answer 3

look it up on the tax assessor's website ... acreage is likely listed there. [or square footage -- there are 43,560 sq ft. in an acre].

[added] if the 120 ft sides are parallel, you have 11,340 sq feet here or 0.2603 acre. however, such calculations breakdown if the 120 ft sides are not parallel and you have to use trigonometry and the sizes of the angles to calculate the area. the tax assessor has already done it in my area.