determining the area of a polygonal field using only the tape

Field Work No. 4[determining the area of a polygonal field using only the tape]

FIELD WORK NO. 4Determining the area of a polygonal field using only the tapeOBJECTIVES:1. To develop the skills in determining the horizontal distance of a uneven ground by breaking the tape method up and down the slope.2. To acquire the skills in determining the horizontal distance of a sloping ground by using the tape and the automatic level.3. To to apply the value of excellence and patience in measuring the distance of the ground.

REASERCH 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.So how to do it?One approach is to break the shape up into pieces that youcansolve - 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 addIn 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 subtractIn 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 shapesIn 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. (assuming of course that the lines that look parallel really are!)

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 verticesIf 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). There is also a computeralgorithmthat does the same.

INSTRUMENTS NEEDED:

Qty.MaterialIllustrationdescription

2 pcs.

Range PolesA range pole, which may also be called a lining pole, is a pole painted with alternating stripes of different colors in consistent widths used often to site measurements. The tool may be a common one for surveyors, where the colors for the stripes are usually red and white or red and yellow. The colors are picked based on their visibility. One end of the pole will typically have either a pointed tip or gripping shoe to aid in standing it on edge. Longer range poles may be equipped with a tripod or stand.

3 pcs.

Chalkis a soft, white, porous sedimentary rock, a form of limestone composed of the mineral calcite. This is used in marking measurements on ground.

2 Pcs.

Plumb bobsA plumb bob is a tool used to ensure that a building structure like a door frame or a shelving support is as vertical as possible. It is also used to measure if an object is placed directly under a point above it, such as placing a shower drain relative to some point on the ceiling, or putting something right under a lighting fixture.

1 pc.

50 meter tapeA tape measure or measuring tape is a flexible form of ruler. It consists of a ribbon of cloth, plastic, fiber glass, or metal strip with linear-measurement markings. It is a common measuring tool. Its flexibility allows for a measure of great length to be easily carried in pocket or toolkit and permits one to measure around curves or corners. Today it is ubiquitous, even appearing in miniature form as a keychain fob, or novelty item. Surveyors use tape measures in lengths of over 100 m (300+ ft).

PROCEDURE:A. Determination of the area of triangle components using the basic formula. A= B x H 21. The students designates the locations of 5 random points that is likely to be a pentagonal shape.2. The chief of party divides the field area into convenient triangular components and calls them A1 ,A2 and A3.3. For first trial use the basic formula to compute the field and designate this as the base of the triangle.4. Determine the length of the altitude to this base. The determination of the altitude is done by locating a point on this base after dropping a line perpendicular to this from opposite vertex by swaying.5. Record the length of the base and altitude in the fieldwork computation sheet provided.6. Repeat the same procedures 4-6 with the rest of the triangular components of the polygonal field and the sum up the areas.B. Determination of the triangles by using the formula. Area=absinC 21. The same triangular field will be used for this second trial but change the naming of the vertices of polygonal filed. 2. The chief of party divides the field area into convenient triangular components and calls them A1 ,A2 and A3.3. For second use the basic formula in B to compute the field and designate this as the base of the triangle.4. Determine the measurement of the angles between the lines.5. Record the lengths of two sides and and included angle in the field work. Record in the data.6. Repeat procedures 4-6 with the rest of triangular components of the polygonal area to compute the entire area.

C. Determination of the area using the formula.

1. The same triangular field will be used for this second trial but change the naming of the vertices of polygonal filed. 2. The chief of party divides the field area into convenient triangular components and calls them A1 ,A2 and A3.3. For third use the basic formula in C the herons formula to compute the field and designate this as the base of the triangle.4. Record the lengths of the three sides of each triangles.5. Repeat procedures 3-5 with the rest of the triangular components until the data is complete.

COMPUTATIONS:

A= area of the triangle B= Base of the triangle H= Altitude of the triangle

A= area of the triangleb and a = random two sides of the trianglesin = sine of the included angle of the measured sides a and b

A= area in triangle in square metersS = half perimeter of trianglea,b and c= sides of the triangles

PRINCIPLE There are several ways that we can measure the distance of the ground. It can be accomplished by breaking the tape method, by making a irregular polygon. A horizontal line of sight is established if the bubble is centered while sigthing through the tube. This device is simply a level adopted for measuring vertical angles. Vertical aide is acted on where angles are read. It gives the value and the slope in terms of arc measure.

Final Data Sheet

A) 1st method: By base and altitudeTriangleBaseAltitudeArea

121.9m12.1m132.485sqm

221.9m14.4m156.68sqm

321.9m8.6m93.68sqm

Total382.845sqm

B) 2nd method by two sides and included angleTriangleAngle in SidesArea

ab

182.8917.55m15.2m132.39sqm

290.9721.9m21.8m156.51sqm

3100.7117.6m10.75m92.95sqm

Total381.80sqm

C)3rd method: By herons formulaTriangleSidesSemi perimeterArea

abcs

117.55m15.2m21.9m27.325m132.55sqm

221.9m21.8m15.86m29.58m157.97sqm

310.75m17.6m21.8m25.058m93.77sqm

Total384.29sqm

ILLUSTRATION

Marking the 5points of the polygon.

Measuring the field by breaking the tape method.

CONCLUSION Based on my own observation to get more accurate results you need to measure the measurement slowly and carefully to obtain better results. You may also measure along the ground on a. But to obtain horizontal distances, you will need to correct these ground measurements afterwards by using correct mathematical formulas . As an additional information we must also apply the value of patience in making the task because the location is outside so expect extreme heat or rain. Calculate all solutions properly and make the distance measured more accurate. We need to be patient and follow all the procedures carefully to make the measurement accurate.