LESSON 2
PERFORM ESTIMATION AND BASIC CALCULATION
LEARNING OUTCOMES:
LO 1. perform estimation
LO 2. perform basic workplace calculation.
Definition of Terms
LO 2. perform basic workplace calculation.
Definition of Terms
- Area - refers to the size of the surface
- Fertilizer - any material added to the soil to support nutrient
- Germination- the development of the seed into a young plant
- Graph- a drawing in which the relationship between two (or more) items of information (e.g. Time and plant growth) is shown in a symbolic way.
- Gross Income/Sales - the equivalent value of the product sold.
- Interest- is the corresponding value that will be added to the principal as payment for using money of the lender.
- Labor- refers to the work performed by farm workers in exchange for salary.
- Net Income- is the value remains after all the expenses have been deducted from the gross income or sales.
- Principal –refers to the amount you owed.
- Volume- is the content of a body or object
Acronyms
- MAD( Man Animal Day) refers to the number of day/s the work will be completed by 1 person and 1 animal.
- MD-(Manday) refers to the number of day/s the work will be completed by 1 person
LEARNING OUTCOME 1
Perform Estimation
PERFORMANCE STANDARDS
- Job requirements are identified from written or oral communications.
- Quantities of materials and resources required to complete a work task are estimated.
- Time needed to complete a work activity is estimated. Accurate estimate for work completion are made.
- Estimate of materials and resources are reported to appropriate person.
- Determine the cost and return of producing horticultural crops.
- Determine the profit/loss using the four fundamental operations.
- Determine the price of a product with the use of mark up percentage.
FARM INPUTS
Seeds Seedlings Fertilizer Insecticide
FARM LABOR
LABOR REQUIREMENT FOR LAND PREPARATION
Plowing using tractor Clearing of the land using hoe Plowing using animal
Harrowing using hand tractor Preparation of Furrow Trellis Preparation (for cucurbit crops)
Mulching Digging Holes (for orchard)
LABOR REQUIREMENT IN PLANTING
PRODUCTION OF SEEDLINGS TRANSPLANTING
LABOR REQUIREMENT FOR PLANT CARE
FERTILIZER APPLICATION PEST CONTROL IRRIGATION
WEEDING HARVESTING
LEARNING OUTCOME 2
Perform basic workplace calculations
PERFORMANCE STANDARDS
- Calculations to be made are identified according to job requirements
- Correct method of calculation is determined.
- Systems and units of measurement to be followed are ascertained.
- Calculations needed to complete work task are performed using the four basic mathematical operations.
- Appropriate operations are used to comply with the instructions.
- Result obtained is reviewed and thoroughly checked
PERFORM CALCULATION
It is important to be able to measure and calculate surface areas. It might be necessary to calculate, for example, the surface area of the cross-section of a canal or the surface area of a farm.
This Section will discuss the calculation of some of the most common surface areas: the triangle, the square, the rectangle, the rhombus, the parallelogram, the trapezium, and the circle.
This Section will discuss the calculation of some of the most common surface areas: the triangle, the square, the rectangle, the rhombus, the parallelogram, the trapezium, and the circle.
The most common surface areas
The height (h) of a triangle, a rhombus, a parallelogram or a trapezium, is the distance from a top corner to the opposite side called base (b). The height is always perpendicular to the base; in other words, the height makes a "right angle" with the base. An example of a right angle is the corner of this page.
In the case of a square or a rectangle, the expression length (l) is commonly used instead of base and width (w) instead of height. In the case of a circle the expression diameter (d) is used.
In the case of a square or a rectangle, the expression length (l) is commonly used instead of base and width (w) instead of height. In the case of a circle the expression diameter (d) is used.
The height (h), base (b), width (w), length (l) and diameter (d) of the most common surface areas
TRIANGLES
The surface area or surface (A) of a triangle is calculated by the formula:
A (triangle) = 0.5 x base x height = 0.5 x b x h ..... (1)
Triangles can have many shapes but the same formula is used for all of them.
Some examples of triangles
EXAMPLE
Calculate the surface area of the triangles no. 1, no. 1a and no. 2
Given Answer
Triangles no. 1 and no. 1a: base = 3 cm Formula: A = 0.5 x base x height
height = 2 cm = 0.5 x 3 cm x 2 cm= 3 cm2
Triangle no. 2: base =3 cm A = 0.5 x 3 cm x 2 cm = 3 cm2
height = 2 cm
It can be seen that triangles no. 1, no. 1a and no. 2 have the same surface; the shapes of the triangles are different, but the base and the height are in all three cases the same, so the surface is the same.
The surface of these triangles is expressed in square centimeters (written as cm2 ). Surface areas can also be expressed in square decimeters (dm2 ), square meters (m2 ), etc...
QUESTION
Calculate the surface areas of the triangles nos. 3, 4, 5 and 6.
Given Answer
Triangle no. 3: base =3 cm Formula: A = 0.5 x base x height
height = 2 cm = 0.5 x 3 cm x 2 cm = 3 cm2
Triangle no. 4: base = 4 cm A = 0.5 x 4 cm x 1 cm = 2 cm2
height = 1 cm
Triangle no. 5: base = 2 cm A = 0.5 x 2 cm x 3 cm = 3 cm2
height = 3 cm
Triangle no. 6: base = 4 cm A = 0.5 x 4 cm x 3 cm = 6 cm2
height = 3 cm
SQUARES AND RECTANGLES
The surface area or surface (A) of a square or a rectangle is calculated by the formula:
A (square or rectangle) = length x width = l x w ..... (2)
In a square the lengths of all four sides are equal and all four angles are right angles.
In a rectangle, the lengths of the opposite sides are equal and all four angles are right angles.
A square and a rectangle
The surface area or surface (A) of a square or a rectangle is calculated by the formula:
A (square or rectangle) = length x width = l x w ..... (2)
In a square the lengths of all four sides are equal and all four angles are right angles.
In a rectangle, the lengths of the opposite sides are equal and all four angles are right angles.
A square and a rectangle
Note that in a square the length and width are equal and that in a rectangle the length and width are not equal.
QUESTION
Calculate the surface areas of the rectangle and of the square.
Given Answer
Square: length = 2 cm Formula: A = length x width
width = 2 cm = 2 cm x 2 cm = 4 cm2
Rectangle: length = 5 cm Formula: A = length x width
width = 3 cm = 5 cm x 3 cm = 15 cm2
Related to irrigation, you will often come across the expression hectare (ha), which is a surface area unit. By definition, 1 hectare equals 10 000 m2 . For example, a field with a length of 100 m and a width of 100 m2 has a surface area of 100 m x 100 m = 10 000 m2 = 1 ha.
Fig. 4. One hectare equals 10 000 m2
QUESTION
Calculate the surface areas of the rectangle and of the square.
Given Answer
Square: length = 2 cm Formula: A = length x width
width = 2 cm = 2 cm x 2 cm = 4 cm2
Rectangle: length = 5 cm Formula: A = length x width
width = 3 cm = 5 cm x 3 cm = 15 cm2
Related to irrigation, you will often come across the expression hectare (ha), which is a surface area unit. By definition, 1 hectare equals 10 000 m2 . For example, a field with a length of 100 m and a width of 100 m2 has a surface area of 100 m x 100 m = 10 000 m2 = 1 ha.
Fig. 4. One hectare equals 10 000 m2
RHOMBUSES AND PARALLELOGRAMS
The surface area or surface (A) of a rhombus or a parallelogram is calculated by the formula:
A (rhombus or parallelogram) = base x height = b x h ..... (3)
In a rhombus the lengths of all four sides are equal; none of the angles are right angles; opposite sides run parallel.
In a parallelogram the lengths of the opposite sides are equal; none of the angles are right angles; opposite sides run parallel.
A rhombus and a parallelogram
The surface area or surface (A) of a rhombus or a parallelogram is calculated by the formula:
A (rhombus or parallelogram) = base x height = b x h ..... (3)
In a rhombus the lengths of all four sides are equal; none of the angles are right angles; opposite sides run parallel.
In a parallelogram the lengths of the opposite sides are equal; none of the angles are right angles; opposite sides run parallel.
A rhombus and a parallelogram
QUESTION
Calculate the surface areas of the rhombus and the parallelogram.
Given Answer
Rhombus: base = 3 cm Formula: A = base x height
height = 2 cm = 3 cm x 2 cm = 6 cm2
Parallelogram: base = 3.5 cm Formula: A = base x height
height = 3 cm = 3.5 cm x 3 cm = 10.5 cm2
1.1.4 TRAPEZIUMS
The surface area or surface (A) of a trapezium is calculated by the formula:
A (trapezium) = 0.5 (base + top) x height =0.5 (b + a) x h ..... (4)
The top (a) is the side opposite and parallel to the base (b). In a trapezium only the base and the top run parallel.
Some examples are shown below: Some examples of trapeziums
EXAMPLE
Calculate the surface area of trapezium no. 1.
Given Answer
Trapezium no. 1: base = 4 cm Formula: A =0.5 x (base x top) x height
top = 2 cm = 0.5 x (4 cm + 2 cm) x 2 cm
height = 2 cm = 0.5 x 6 cm x 2 cm = 6 cm2
QUESTION
Calculate the surface areas trapeziums nos. 2, 3 and 4.
Given Answer
Trapezium no. 2: base = 5 cm Formula: A = 0.5 x (base + top) x height
top = 1 cm = 0.5 x (5 cm + 1 cm) x 2 cm
height = 2 cm = 0.5 x 6 cm x 2 cm = 6 cm2
Trapezium no. 3: base = 3 cm A = 0.5 x (3 cm + 1 cm) x 2 cm
top = 1 cm = 0.5 x 4 cm x 2 cm = 4 cm2
height = 1 cm
Trapezium no. 4: base = 2 cm A = 0.5 x (2 cm + 4 cm) x 2 cm
top = 4 cm = 0.5 x 6 cm x 2 cm = 6 cm2
height = 2 cm
Note that the surface areas of the trapeziums 1 and 4 are equal. Number 4 is the same as number 1 but upside down.
Another method to calculate the surface area of a trapezium is to divide the trapezium into a rectangle and two triangles, to measure their sides and to determine separately the surface areas of the rectangle and the two triangles. Splitting a trapezium into one rectangle and two triangles.
Splitting a trapezium into one rectangle and two triangles. Note that A = A1+ A2 + A3 = 1 + 6 + 2 =9 cm2
Calculate the surface area of trapezium no. 1.
Given Answer
Trapezium no. 1: base = 4 cm Formula: A =0.5 x (base x top) x height
top = 2 cm = 0.5 x (4 cm + 2 cm) x 2 cm
height = 2 cm = 0.5 x 6 cm x 2 cm = 6 cm2
QUESTION
Calculate the surface areas trapeziums nos. 2, 3 and 4.
Given Answer
Trapezium no. 2: base = 5 cm Formula: A = 0.5 x (base + top) x height
top = 1 cm = 0.5 x (5 cm + 1 cm) x 2 cm
height = 2 cm = 0.5 x 6 cm x 2 cm = 6 cm2
Trapezium no. 3: base = 3 cm A = 0.5 x (3 cm + 1 cm) x 2 cm
top = 1 cm = 0.5 x 4 cm x 2 cm = 4 cm2
height = 1 cm
Trapezium no. 4: base = 2 cm A = 0.5 x (2 cm + 4 cm) x 2 cm
top = 4 cm = 0.5 x 6 cm x 2 cm = 6 cm2
height = 2 cm
Note that the surface areas of the trapeziums 1 and 4 are equal. Number 4 is the same as number 1 but upside down.
Another method to calculate the surface area of a trapezium is to divide the trapezium into a rectangle and two triangles, to measure their sides and to determine separately the surface areas of the rectangle and the two triangles. Splitting a trapezium into one rectangle and two triangles.
Splitting a trapezium into one rectangle and two triangles. Note that A = A1+ A2 + A3 = 1 + 6 + 2 =9 cm2
1.1.5 CIRCLES
The surface area or surface (A) of a circle is calculated by the formula:
A (circle) = 1/4 (¶ x d x d) = 1/4 (¶ x d2 ) = 1/4 (3.14 x d2 ) ..... (5)
whereby d is the diameter of the circle and ¶ (a Greek letter, pronounced Pi) a constant (¶ = 3.14). A diameter (d) is a straight line which divides the circle in two equal parts.
A circle
The surface area or surface (A) of a circle is calculated by the formula:
A (circle) = 1/4 (¶ x d x d) = 1/4 (¶ x d2 ) = 1/4 (3.14 x d2 ) ..... (5)
whereby d is the diameter of the circle and ¶ (a Greek letter, pronounced Pi) a constant (¶ = 3.14). A diameter (d) is a straight line which divides the circle in two equal parts.
A circle
EXAMPLE
Given Answer
Circle: d = 4.5 cm Formula: A = 1/4 (¶ x d²)
= 1/4 (3.14 x d x d)
= 1/4 (3.14 x 4.5 cm x 4.5 cm)
= 15.9 cm2
QUESTION
Calculate the surface area of a circle with a diameter of 3 m.
Given Answer
Circle: d = 3 m Formula: A = 1/4 (¶ x d²)
= 1/4 (3.14 x d x d)
= 1/4 (3.14 x 3 m x 3 m)
= 7.07 m2
METRIC CONVERSIONS
Units of length
The basic unit of length in the metric system is the meter (m). One meter can be divided into 10 decimeters (dm), 100 centimeters (cm) or 1000 millimeters (mm); 100 m equals to 1 hectometer (hm); while 1000 m is 1 kilometer (km).
1 m = 10 dm = 100 cm = 1000 mm
0.1 m = 1 dm = 10 cm = 100 mm
0.01 m = 0.1 dm = 1 cm = 10 mm
0.001 m = 0.01 dm = 0.1 cm =
1 mm 1 km = 10 hm = 1000 m
0.1 km = 1 hm = 100 m
0.01 km = 0.1 hm = 10 m
0.001 km = 0.01 hm = 1 m
Units of surface
The basic unit of area in the metric system is the square meter (m), which is obtained by multiplying a length of 1 meter by a width of 1 meter.
A square meter
1 m2 = 100 dm2 = 10 000 cm2 = 1 000 000 mm 2
0.01 m2 = 1 dm2 = 100 cm2 = 10 000 mm2
0.0001 m2 = 0.01 dm2 = 1 cm2 = 100 mm2
0.000001 m2 = 0.0001 dm2 = 0.01 cm2 = 1 mm2
1 km2 = 100 ha2 = 1 000 000 m2
0.01 km2 = 1 ha2 = 10 000 m2
0.000001 km2 = 0.0001 ha2 = 1 m2
NOTE:
1 ha =100 m x 100 m = 10 000 m2
SURFACE AREAS OF CANAL CROSS-SECTIONS AND FARMS
This section explains how to apply the surface area formulas to two common practical problems that will often be met in the field.
DETERMINATION OF THE SURFACE AREAS OF CANAL CROSS-SECTIONS
The most common shape of a canal cross-section is a trapezium or, more truly, an "up-sidedown" trapezium.
Canal crosssection
0.01 m2 = 1 dm2 = 100 cm2 = 10 000 mm2
0.0001 m2 = 0.01 dm2 = 1 cm2 = 100 mm2
0.000001 m2 = 0.0001 dm2 = 0.01 cm2 = 1 mm2
1 km2 = 100 ha2 = 1 000 000 m2
0.01 km2 = 1 ha2 = 10 000 m2
0.000001 km2 = 0.0001 ha2 = 1 m2
NOTE:
1 ha =100 m x 100 m = 10 000 m2
SURFACE AREAS OF CANAL CROSS-SECTIONS AND FARMS
This section explains how to apply the surface area formulas to two common practical problems that will often be met in the field.
DETERMINATION OF THE SURFACE AREAS OF CANAL CROSS-SECTIONS
The most common shape of a canal cross-section is a trapezium or, more truly, an "up-sidedown" trapezium.
Canal crosssection
The area (A B C D), hatched on the above drawing, is called the canal cross-section and has a trapezium shape. Thus, the formula to calculate its surface is similar to the formula used to calculate the surface area of a trapezium:
Surface area of the canal cross-section = 0.5 (base + top line) x canal depth = 0.5 (b + a) x h ..... (6)
whereby:
base (b) = bottom width of the canal
top line (a) = top width of the canal
canal depth (h) = height of the canal (from the bottom of the canal to the top of the embankment)
Suppose that the canal contains water, as shown in Figure below.
Wetted cross-section of a canal
Surface area of the canal cross-section = 0.5 (base + top line) x canal depth = 0.5 (b + a) x h ..... (6)
whereby:
base (b) = bottom width of the canal
top line (a) = top width of the canal
canal depth (h) = height of the canal (from the bottom of the canal to the top of the embankment)
Suppose that the canal contains water, as shown in Figure below.
Wetted cross-section of a canal
The area (A B C D), hatched on the above drawing, is called the wetted canal crosssection or wetted cross-section. It also has a trapezium shape and the formula to calculate its surface area is:
Surface area of the wetted canal cross-section = 0.5 (base + top line) x water depth = 0.5 (b + a1) x h1 ..... (7)
whereby:
base (b) = bottom width of the canal
top line (a1) = top width of the water level
water depth (h1) = the height or depth of the water in the canal (from the bottom of the canal to the water level).
EXAMPLE
Calculate the surface area of the cross-section and the wetted cross-section, of the canal shown in next figure.
Dimensions of the cross-section
Surface area of the wetted canal cross-section = 0.5 (base + top line) x water depth = 0.5 (b + a1) x h1 ..... (7)
whereby:
base (b) = bottom width of the canal
top line (a1) = top width of the water level
water depth (h1) = the height or depth of the water in the canal (from the bottom of the canal to the water level).
EXAMPLE
Calculate the surface area of the cross-section and the wetted cross-section, of the canal shown in next figure.
Dimensions of the cross-section
Given Answer
Canal cross-section:
base (b) =1.25 m Formula: A = 0.5 x (b + a) x h
top line (a) =3.75 m = 0.5 x (1.25 m + 3.75 m) x 1.25 m
canal depth (h) = 1.25 m = 3.125 m2
Canal wetted cross-section:
base (b) = 1.25 m Formula: A = 0.5 x (b + a1) x h
top line (a1) = 3.25 m = 0.5 x (1.25 m + 3.25 m) x 1.00 m
water depth (h1) =1.00 m = 2.25 m2
DETERMINATION OF THE SURFACE AREA OF A FARM
It may be necessary to determine the surface area of a farmer's field. For example, when calculating how much irrigation water should be given to a certain field, the size of the field must be known.
When the shape of the field is regular and has, for example, a rectangular shape, it should not be too difficult to calculate the surface area once the length of the field (that is the base of its regular shape) and the width of the field have been measured.
Field of regular shape
EXAMPLE