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’
I
94’
12’
III
16’
II
29’
42’
Try these three –
4’
I
94’
12’
III
16’
3,948 ft2
48
ft2
II
464 ft2
29’
42’
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
H
A=
2
16’
L
x
H
A=
2
12’
12
x
16
A=
2
16’
L
x
H
A=
2
12’
12
x
16
A=
2
16’
A = 96
12’
2
ft
Try these…
41’
II
19’
10’ I
11’
121’
III
212’
Try these…
389.5ft2
41’
II
55ft2
19’
12,826ft2
10’ I
11’
121’
III
212’
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…
44’
80’
61’
Determine the length of the three
sides of the field…
44’
80’
61’
And use the following formula:
44’
80’
61’
A=
s(s-a)(s-b)(s-c)
a+b+c
Where s =
2
44’
80’
61’
a, b, and c are
the three sides of
the triangle
44’
80’
a, b, and c are
the three sides of
the triangle
61’
First, determine ‘s’
a+b+c
s=
2
44’
80’
a, b, and c are
the three sides of
the triangle
61’
First, determine ‘s’
44+80+61
s=
2
44’
80’
a, b, and c are
the three sides of
the triangle
61’
First, determine ‘s’
44+80+61
s=
2
185
s=
2
44’
80’
a, b, and c are
the three sides of
the triangle
61’
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:
A=
92.5(92.5-44)(92.5-80)(92.5-61)
Then, following standard order of
operations, do the math!
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(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=
1,766,460.9
A=
92.5(92.5-44)(92.5-80)(92.5-61)
A=
92.5(48.5)(12.5)(31.5)
A=
1,766,460.9
A=
1329.08 ft2