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

ELEMENTARY SURVEYING FIELD MANUAL

FIELD WORK NO. 4 DETERMINING 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 TIME: 8:30AM – 12:00PM WEATHER: SUNNY

GROUP NO.: 4 LOCATION: MAPUA CAMPUS PROFESSOR: ENGR. CERVANTES

A. 1ST METHOD: BY BASE AND ALTITUDE METHOD TRIANGLE 1 2 3

BASE 5.2 m 5.2 m 6.36 m

ALTITUDE 2.2 m 4.87 m 2.71 m TOTAL

AREA 5.72 m2 12.662 m2 8.618 m2 27 m2

B. COMPUTATIONS:

ATRIANGLE1 = ATRIANGLE1 =

1 2 1 2

bh

Total Area = ATRIANGLE1 + ATRIANGLE2 + ATRIANGLE3

(5.2 m) (2.2 m)

Total Area = (5.72 m2) + (12.662 m2) + (8.618 m2) Total Area = 27 m2

ATRIANGLE1 = 5.72 m2

C. 2ND METHOD: BY TWO SIDES AND THE INCLUDED ANGLE TRIANGLE 1 2 3

ANGLE θ in degrees 98.713° 51.572° 52.208°

SIDES a 3.5 m 5.2 m 3.5 m

AREA b 3.3 m 6.36 m 6.36 m TOTAL

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5.708 m2 12.954 m2 8.795 m2 27.457 m2

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

D. COMPUTATIONS: ATRIANGLE1 = ATRIANGLE1 = (98.713°)

1 2 1 2

ab sin θ

Total Area = ATRIANGLE1 + ATRIANGLE2 + ATRIANGLE3

(3.5 m) (3.3 m) sin

Total Area = (5.708 m2) + (12.954 m2) + (8.795 m2) Total Area = 27.457 m2

ATRIANGLE1 = 5.708 m2

E. 3RD METHOD: BY THREE SIDES (HERON’S FORMULA) TRIANGLE

1 2 3

SIDES a 3.5 m 5.2 m 6.36 m

b 5.3 m 4.83 m 3.5 m

c 3.2 m 6.36 m 4.87 m

F. COMPUTATIONS: ATRIANGLE1 =

s s − a s − b (s − c)

ATRIANGLE1 =

6 6 − 3.5 6 − 5.3 (6 − 3.2)

ATRIANGLE1 = 5.62 m2

Total Area = ATRIANGLE1 + ATRIANGLE2 + ATRIANGLE3 Total Area = (5.62 m2) + (12.311 m2) + (8.448 m2) Total Area = 26.451 m2

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HALF PARAMETER s 6m 8.195 m 7.365 m TOTAL

AREA 5.62 m2 12.311 m2 8.448 m2 26.451 m2

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

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

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

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

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

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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