Area & Volumetric Determination. A Point No length, no width, no depth.. No Dimensions.
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Transcript of Area & Volumetric Determination. A Point No length, no width, no depth.. No Dimensions.
![Page 1: Area & Volumetric Determination. A Point No length, no width, no depth.. No Dimensions.](https://reader036.fdocuments.us/reader036/viewer/2022062321/56649f2f5503460f94c49bec/html5/thumbnails/1.jpg)
Area & Volumetric Determination
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![Page 3: Area & Volumetric Determination. A Point No length, no width, no depth.. No Dimensions.](https://reader036.fdocuments.us/reader036/viewer/2022062321/56649f2f5503460f94c49bec/html5/thumbnails/3.jpg)
A Point
![Page 4: Area & Volumetric Determination. A Point No length, no width, no depth.. No Dimensions.](https://reader036.fdocuments.us/reader036/viewer/2022062321/56649f2f5503460f94c49bec/html5/thumbnails/4.jpg)
A Point
No length, no width, no depth..
No Dimensions
![Page 5: Area & Volumetric Determination. A Point No length, no width, no depth.. No Dimensions.](https://reader036.fdocuments.us/reader036/viewer/2022062321/56649f2f5503460f94c49bec/html5/thumbnails/5.jpg)
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A Line
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A Line
It has one dimension: length
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A rectangle, or plane
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A rectangle, or plane
This geometric figure has two dimensions: length and heigth. It is, therefore, two dimensional.
![Page 11: Area & Volumetric Determination. A Point No length, no width, no depth.. No Dimensions.](https://reader036.fdocuments.us/reader036/viewer/2022062321/56649f2f5503460f94c49bec/html5/thumbnails/11.jpg)
A rectangle, or plane
The area of any four sided figure having four 90 degree angles can be determined
by…
![Page 12: Area & Volumetric Determination. A Point No length, no width, no depth.. No Dimensions.](https://reader036.fdocuments.us/reader036/viewer/2022062321/56649f2f5503460f94c49bec/html5/thumbnails/12.jpg)
A rectangle, or plane
The area of any four sided figure having four 90 degree angles can be determined
by…
A=LxW
![Page 13: Area & Volumetric Determination. A Point No length, no width, no depth.. No Dimensions.](https://reader036.fdocuments.us/reader036/viewer/2022062321/56649f2f5503460f94c49bec/html5/thumbnails/13.jpg)
Try these three –
4’
12’I
II
III16’
29’
94’
42’
![Page 14: Area & Volumetric Determination. A Point No length, no width, no depth.. No Dimensions.](https://reader036.fdocuments.us/reader036/viewer/2022062321/56649f2f5503460f94c49bec/html5/thumbnails/14.jpg)
Try these three –
4’
12’I
II
III16’
29’
94’
42’
48 ft2
464 ft2
3,948 ft2
![Page 15: Area & Volumetric Determination. A Point No length, no width, no depth.. No Dimensions.](https://reader036.fdocuments.us/reader036/viewer/2022062321/56649f2f5503460f94c49bec/html5/thumbnails/15.jpg)
The area of virtually any geometric figure can be determined by breaking
the figure up into triangles.
![Page 16: Area & Volumetric Determination. A Point No length, no width, no depth.. No Dimensions.](https://reader036.fdocuments.us/reader036/viewer/2022062321/56649f2f5503460f94c49bec/html5/thumbnails/16.jpg)
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
![Page 17: Area & Volumetric Determination. A Point No length, no width, no depth.. No Dimensions.](https://reader036.fdocuments.us/reader036/viewer/2022062321/56649f2f5503460f94c49bec/html5/thumbnails/17.jpg)
If you had a field that looked like this, and needed to know how many acres were in it….
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And all you had to use was a simple measuring tape…
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You could break the field up into triangles like this…
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Leaving you with six fairly simple calculations that you would add together…
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The area of a simple right triangle can be determined by using the formula…
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The area of a simple right triangle can be determined by using the formula…
L x H2
A=
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L x H2
A=
16’
12’
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L x H2
A=
16’
12’
12 x 162
A=
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16’
12’
12 x 162
A=
A = 96 ft2
![Page 30: Area & Volumetric Determination. A Point No length, no width, no depth.. No Dimensions.](https://reader036.fdocuments.us/reader036/viewer/2022062321/56649f2f5503460f94c49bec/html5/thumbnails/30.jpg)
Try these…
I
II
III10’
11’
41’
19’
121’ 212’
![Page 31: Area & Volumetric Determination. A Point No length, no width, no depth.. No Dimensions.](https://reader036.fdocuments.us/reader036/viewer/2022062321/56649f2f5503460f94c49bec/html5/thumbnails/31.jpg)
Try these…
I
II
III10’
11’
41’
19’
121’ 212’
55ft2
389.5ft2
12,826ft2
![Page 32: Area & Volumetric Determination. A Point No length, no width, no depth.. No Dimensions.](https://reader036.fdocuments.us/reader036/viewer/2022062321/56649f2f5503460f94c49bec/html5/thumbnails/32.jpg)
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….
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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….
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Determine the length of the three sides of the field…
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Determine the length of the three sides of the field…
44’
61’
80’
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And use the following formula:
44’
61’
80’
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44’
61’
80’
s(s-a)(s-b)(s-c)A=
Where s = a+b+c2
![Page 38: Area & Volumetric Determination. A Point No length, no width, no depth.. No Dimensions.](https://reader036.fdocuments.us/reader036/viewer/2022062321/56649f2f5503460f94c49bec/html5/thumbnails/38.jpg)
44’
61’
80’ a, b, and c are the three sides of the triangle
![Page 39: Area & Volumetric Determination. A Point No length, no width, no depth.. No Dimensions.](https://reader036.fdocuments.us/reader036/viewer/2022062321/56649f2f5503460f94c49bec/html5/thumbnails/39.jpg)
44’
61’
80’ a, b, and c are the three sides of the triangle
First, determine ‘s’
s = a+b+c2
![Page 40: Area & Volumetric Determination. A Point No length, no width, no depth.. No Dimensions.](https://reader036.fdocuments.us/reader036/viewer/2022062321/56649f2f5503460f94c49bec/html5/thumbnails/40.jpg)
44’
61’
80’ a, b, and c are the three sides of the triangle
First, determine ‘s’
s = 44+80+612
![Page 41: Area & Volumetric Determination. A Point No length, no width, no depth.. No Dimensions.](https://reader036.fdocuments.us/reader036/viewer/2022062321/56649f2f5503460f94c49bec/html5/thumbnails/41.jpg)
44’
61’
80’ a, b, and c are the three sides of the triangle
First, determine ‘s’
s = 44+80+612 s = 185
2
![Page 42: Area & Volumetric Determination. A Point No length, no width, no depth.. No Dimensions.](https://reader036.fdocuments.us/reader036/viewer/2022062321/56649f2f5503460f94c49bec/html5/thumbnails/42.jpg)
44’
61’
80’ a, b, and c are the three sides of the triangle
First, determine ‘s’
s = 92.5
![Page 43: Area & Volumetric Determination. A Point No length, no width, no depth.. No Dimensions.](https://reader036.fdocuments.us/reader036/viewer/2022062321/56649f2f5503460f94c49bec/html5/thumbnails/43.jpg)
Now that you have all the numbers you need, plug them into the formula, like so:
![Page 44: Area & Volumetric Determination. A Point No length, no width, no depth.. No Dimensions.](https://reader036.fdocuments.us/reader036/viewer/2022062321/56649f2f5503460f94c49bec/html5/thumbnails/44.jpg)
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=
![Page 45: Area & Volumetric Determination. A Point No length, no width, no depth.. No Dimensions.](https://reader036.fdocuments.us/reader036/viewer/2022062321/56649f2f5503460f94c49bec/html5/thumbnails/45.jpg)
Then, following standard order of operations, do the math!
92.5(92.5-44)(92.5-80)(92.5-61)A=
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92.5(92.5-44)(92.5-80)(92.5-61)A=
![Page 47: Area & Volumetric Determination. A Point No length, no width, no depth.. No Dimensions.](https://reader036.fdocuments.us/reader036/viewer/2022062321/56649f2f5503460f94c49bec/html5/thumbnails/47.jpg)
92.5(92.5-44)(92.5-80)(92.5-61)A=
92.5(48.5)(12.5)(31.5)A=
![Page 48: Area & Volumetric Determination. A Point No length, no width, no depth.. No Dimensions.](https://reader036.fdocuments.us/reader036/viewer/2022062321/56649f2f5503460f94c49bec/html5/thumbnails/48.jpg)
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=
![Page 49: Area & Volumetric Determination. A Point No length, no width, no depth.. No Dimensions.](https://reader036.fdocuments.us/reader036/viewer/2022062321/56649f2f5503460f94c49bec/html5/thumbnails/49.jpg)
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