FIELD WORK NO. 4 DETERMINING THE AREA OF A POLYGONAL FIELD USING ONLY THE TAPE.pdf

8/10/2019 FIELD WORK NO. 4 DETERMINING THE AREA OF A POLYGONAL FIELD USING ONLY THE TAPE.pdf

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ELEMENTARY SURVEYING FIELD

MANUAL

FIELD WORK NO. 4DETERMINING THE AREA OF A POLYGONAL

FIELD USING ONLY THE TAPE

CE120-0F / A1

SUBMITTED BY:

NAME: STUDENT NO.:

GROUP NO. 4

DATE OF FIELD WORK: AUGUST 7, 2014

DATE OF SUBMITTION: AUGUST 14, 2014

CHIEF OF PARTY:

SUBMITTED TO:

PROFESSOR: ENGR. CERVANTES

GRADE


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FIELD WORK NO. 4 DETERMING THE AREA OF A POLYGONAL FIELD USING ONLY THE TAPE

FINAL DATE SHEET

FIELD WORK 4 DETERMINING THE AREA OF A POLYGONAL FIELD

DATE: AUGUST 7, 2014 GROUP NO.: 4TIME: 8:30AM12:00PM LOCATION: MAPUA CAMPUS

WEATHER: SUNNY PROFESSOR: ENGR. CERVANTES

A. 1STMETHOD: BY BASE AND ALTITUDE METHOD

TRIANGLE BASE ALTITUDE AREA

1 5.2 m 2.2 m 5.72 m

2 5.2 m 4.87 m 12.662 m

3 6.36 m 2.71 m 8.618 m

TOTAL 27 m2

B. COMPUTATIONS:

ATRIANGLE1=1

2bh

ATRIANGLE1=1

2(5.2 m) (2.2 m)

ATRIANGLE1= 5.72 m

Total Area = ATRIANGLE1+ ATRIANGLE2+ATRIANGLE3

Total Area = (5.72 m2) + (12.662 m2) +(8.618 m2)

Total Area = 27 m

C. 2NDMETHOD: BY TWO SIDES AND THE INCLUDED ANGLE

TRIANGLE ANGLE SIDES AREA

in degrees a b

1 98.713 3.5 m 3.3 m 5.708 m

2 51.572 5.2 m 6.36 m 12.954 m

3 52.208 3.5 m 6.36 m 8.795 m

TOTAL 27.457 m


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D. COMPUTATIONS:

ATRIANGLE1=1

2ab sin

ATRIANGLE1=

1

2(3.5 m) (3.3 m) sin(98.713)

ATRIANGLE1= 5.708 m


Total Area = (5.708 m2) + (12.954 m2) +

(8.795 m2)

Total Area = 27.457 m2

E. 3RDMETHOD: BY THREE SIDES (HERONS FORMULA)

TRIANGLE SIDES HALF

PARAMETER

AREA

a b c s

1 3.5 m 5.3 m 3.2 m 6 m 5.62 m

2 5.2 m 4.83 m 6.36 m 8.195 m 12.311 m

3 6.36 m 3.5 m 4.87 m 7.365 m 8.448 m

TOTAL 26.451 m2

F. COMPUTATIONS:

ATRIANGLE1= ssasb(sc)

ATRIANGLE1= 663.565.3(63.2)

ATRIANGLE1= 5.62 m2


Total Area = (5.62 m2) + (12.311 m2) +(8.448 m

2)

Total Area = 26.451 m


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G. SKETCH

Measuring a side of the polygonal field.

Drawing a line from a formed triangle for determining the angle included.


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DESCRIPTION

Irregular polygon is a polygon whose sides are not all the same length or whose

interior angles do not all have the same measure. Unlike a regular polygon, unless you

know the coordinates of the vertices, there is no easy formula for the area of an

irregular polygon. Each side could be a different length, and each interior angle could be

different. It could also be either convex or concave.

So how to determine the area of an irregular polygon? One approach is to break

the shape up into pieces that you can solve - usually triangles, since there are many

ways to calculate the area of triangles. Exactly how you do it depends on what you are

given to start. Since this is highly variable there is no easy rule for how to do it. The

examples below give you some basic approaches to try.

1. Break into triangles, then add

In the figure on the right, the polygon can be broken up into triangles by drawing

all the diagonals from one of the vertices. If you know enough sides and angles to find

the area of each, then you can simply add them up to find the total. Do not be afraid to

draw extra lines anywhere if they will help find shapes you can solve.

2. Find 'missing' triangles, then subtract

In the figure on the left, the overall shape is a regular hexagon, but there is a

triangular piece missing. We know how to find the area of a regular polygon so we just

subtract the area of the 'missing' triangle created by drawing the red line.


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3. Consider other shapes

In the figure on the right, the shape is an irregular hexagon, but it has a

symmetry that lets us break it into two parallelograms by drawing the red dotted line.

We know how to find the area of a parallelogram so we just find the area of each one

and add them together. As you can see, there an infinite number of ways to break down

the shape into pieces that are easier to manage. You then add or subtract the areas of

the pieces. Exactly how you do it comes down to personal preference and what you are

given to start.

4. If you know the coordinates of the vertices

If you know the x,y coordinates of the vertices (corners) of the shape, there is a method

for finding the area directly. This works for all polygon types (regular, irregular, convex,

concave). This method will produce the wrong answer for self-intersecting polygons,


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where one side crosses over another, as shown on the right. It will work correctly

however for triangles, regular and irregular polygons, convex or concave polygons.

The area is then given by the formula,


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CONCLUSION

On this field work, we tried to determine the area of a polygonal field using the

tape only by dividing the area into triangles and using different ways in getting the area.

Based on the data gathered, I observed that the area acquired from the different

methods were different from each other. Although these data are distinct from one

another, they only differ from small amount. The second method which is using two

sides of a triangle and an included angle yielded the largest area while the third method

which is using the three sides of a triangle yielded the smallest area.

According from the lecture being discussed, these methods should have yielded

the same area. The common sources of error on this field work are the inaccurate

reading of measurements and human errors. Human errors include the reading of

measurements of the sides, included angle, and diagonal of the polygonal field even if

the measuring tape is not totally perpendicular to the ground.

It is recommended to have patience in doing the field work because this field

work has so much part and a lot to be done. Also check first if the measuring tape is

completely perpendicular to the ground before recording the measurement to lessen the

error that might be acquired. Using a plumb bob is also recommended to see if the

measuring tape is perpendicular to the ground. Follow the instructions on the manual

carefully to avoid errors.

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FIELD WORK NO. 4 DETERMINING THE AREA OF A POLYGONAL FIELD USING ONLY THE TAPE.pdf