MAPUA INSTITUTE OF TECHNOLOGY

SCHOOL OF CIVIL, ENVIRONMENTAL AND GEOLOGICAL ENGINEERING

SURVEYING 1

Field Work 1PACING ON LEVEL GROUND

COURSE AND SECTION: CE 120-0 / A2

SUBMITTED BY:

Name: DUGUIANG, MARC RAINIER B.

Group No: 4

DATE OF FIELD WORK: 02/03/2015 DATE OF SUBMISSION: 02/10/2015

SUBMITTED TO:

GRADE

ENGR. BIENVENIDO CERVANTES

Objectives:

1. To develop the skills in determining the area of a polygon field using the tape only by dividing the area into triangles.

Instruments:

1. 2 range poles

2. Chalk

3. 50 meter tape

4. Plumb bob

Discussion:

The field work was conducted by measuring 5 lines to form a

pentagon in the field using tape and range poles. In measuring the

distances, the tape must no touch the ground since we are not sure if it’s

leveled or not and what we need to find is its horizontal distance. In

surveying, to measure horizontal distances, we must take note of slopes

and obstacles that make our measurement inaccurate. This is why we must

use range poles and plumb bobs in order to lift the tape and measure it at

an elevation but we must make sure the pole stands straight and the tape

is perpendicular to the pole.

While other members hold the equipment, another looks at a short

distance to make sure that the tape is perpendicular to the range pole. We

also measured diagonals from different points using the same method. In

order to measure for the area of the pentagon, we divided it into three

triangles. And using methods in surveying, we got the altitude of each

triangle and also their interior angles.

To compute the area of the pentagon, we used three different

methods. We used Heron’s formulaA=√s (s−a)(s−b)(s−c ), thenA=12absinθ,

and finallyA=12bh. To test the accuracy of our measurements, we compared

the areas computed using each methods. And as a result, the areas were

all precise.

Conclusion:

There are many ways to measure the area of a polygon. One of the

most convenient way is to divide it into triangles then get the area of each

and then get the sum. In this activity, we used three methods to get the

area of the pentagon. As we compared the results, we found out that the

measurements were accurate and the computed areas were precise.

The tricky part of this activity was to determine the horizontal

distances for each points including the diagonals since sloping distance

might occur when we place the tape on the ground. Therefore, in

surveying, measuring horizontal distances using tape requires the workers

to lift the tape and put it in perpendicular to straight standing poles. When

proper set up of equipment is observed, it is the right time to get the

reading from the tape.

Since the gathered results are precise and accurate, we can

conclude that using tape is an easy method to get area of a polygon. But its

accuracy is only limited by the size of the area, therefore other methods are

required when handling measurements of bigger fields.

FINAL DATA SHEET

FIELD WORK 4 DETERMINING THE AREA OF A POLYGONAL FIELD USING ONLY THE TAPE

DATE: February 3, 2014 GROUP NO. 4TIME: 7:30AM - 12:00NN LOCATION: IntramurosWEATHER: SUNNY PROFESSOR: Engr. B. Cervantes

1ST METHOD: BY BASE AND ALTITUDE METHODA. TRIANGLE BASE ALTITUDE AREA

14.62m

1.3m 3.003

2 3.4m 4.39m 7.4633 4.8m 1.69m 4.056

TOTAL 14.522

B. 2ND METHOD: BY TWO SIDES AND THE INCLUDED ANGLE

TRIANGLE ANGLE SIDES AREAθ in degrees a B

1 25.97 4.62 2.97 3.0042 66.44 3.4 4.8 7.483 70.81 3.2 2.69 4.065

TOTAL 14.55

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

TRIANGLE SIDESHALF

PERIMETERAREA

a b c S1 2.97 2.34 4.62 4.965 2.992 4.62 3.4 4.8 6.41 7.453 4.8 3.2 2.69 5.345 4.07

TOTAL 14.51

Research

Measuring the polygonal field with different sides are called measuring of

irregular polygons. An irregular polygon is any polygon that is not a regular

polygon. It can have sides of any length and each interior angle can be any

measure. They can be convex or concave, but all concave polygons are

irregular since the interior angles cannot all be the same. If you drew a

polygon at random, it would probably be irregular. Specific irregular

polygons such as a parallelogram have some interesting properties and

have their own web pages.

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, and 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. Here, the irregular hexagon is divided in to

4 triangles by the addition of the red lines.

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.

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.