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Area & Volumetric Determination
A Point
A Point
No length, no width, no depth..
No Dimensions
A Line
A Line
It has one dimension: length
A rectangle, or plane
A rectangle, or plane
This geometric figure has two dimensions: length and heigth. It is, therefore, two dimensional.
A rectangle, or plane
The area of any four sided figure having four 90 degree angles can be determined
by…
A rectangle, or plane
The area of any four sided figure having four 90 degree angles can be determined
by…
A=LxW
Try these three –
4’
12’I
II
III16’
29’
94’
42’
Try these three –
4’
12’I
II
III16’
29’
94’
42’
48 ft2
464 ft2
3,948 ft2
The area of virtually any geometric figure can be determined by breaking
the figure up into triangles.
The area of virtually any geometric figure can be determined by breaking
the figure up into triangles.
For instance, take the figure in the middle
If you had a field that looked like this, and needed to know how many acres were in it….
And all you had to use was a simple measuring tape…
You could break the field up into triangles like this…
Leaving you with six fairly simple calculations that you would add together…
The area of a simple right triangle can be determined by using the formula…
The area of a simple right triangle can be determined by using the formula…
L x H2
A=
L x H2
A=
16’
12’
L x H2
A=
16’
12’
12 x 162
A=
16’
12’
12 x 162
A=
A = 96 ft2
Try these…
I
II
III10’
11’
41’
19’
121’ 212’
Try these…
I
II
III10’
11’
41’
19’
121’ 212’
55ft2
389.5ft2
12,826ft2
In real agricultural conditions, true right triangles rarely exist. Unless you have sophisticated equipment, such as a surveyor’s transit, your options for determining the area of a field are limited….
In real agricultural conditions, true right triangles rarely exist. Unless you have sophisticated equipment, such as a surveyor’s transit, your options for determining the area of a field are limited.
The easiest way is to….
Determine the length of the three sides of the field…
Determine the length of the three sides of the field…
44’
61’
80’
And use the following formula:
44’
61’
80’
44’
61’
80’
s(s-a)(s-b)(s-c)A=
Where s = a+b+c2
44’
61’
80’ a, b, and c are the three sides of the triangle
44’
61’
80’ a, b, and c are the three sides of the triangle
First, determine ‘s’
s = a+b+c2
44’
61’
80’ a, b, and c are the three sides of the triangle
First, determine ‘s’
s = 44+80+612
44’
61’
80’ a, b, and c are the three sides of the triangle
First, determine ‘s’
s = 44+80+612 s = 185
2
44’
61’
80’ a, b, and c are the three sides of the triangle
First, determine ‘s’
s = 92.5
Now that you have all the numbers you need, plug them into the formula, like so:
Now that you have all the numbers you need, plug them into the formula, like so:
92.5(92.5-44)(92.5-80)(92.5-61)A=
Then, following standard order of operations, do the math!
92.5(92.5-44)(92.5-80)(92.5-61)A=
92.5(92.5-44)(92.5-80)(92.5-61)A=
92.5(92.5-44)(92.5-80)(92.5-61)A=
92.5(48.5)(12.5)(31.5)A=
92.5(92.5-44)(92.5-80)(92.5-61)A=
92.5(48.5)(12.5)(31.5)A=
1,766,460.9A=
92.5(92.5-44)(92.5-80)(92.5-61)A=
92.5(48.5)(12.5)(31.5)A=
1,766,460.9A=
A= 1329.08 ft2
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