TLE 7 EXPLORATORY

1. SURFACE AREAS
OF CANAL
CROSS-
SECTIONS AND
FARMS
ELAINE JOY F. ANDAYA
Teacher

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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 instruction.
 Result obtained is reviewed and thoroughly checked.

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Determine the following pictures:

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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.

5. 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-side-down" trapezium.
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6. 1. Canal Cross-Sections
The area (A B C D), hatched on the 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.
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7. Formula:
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)
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Surface area of the canal cross-section = 0.5 (base + top line) x
canal depth = 0.5 (b + a) x h ..... (6)

8. Wetted Cross-Section of a Canal
The area (A B C D), hatched on the drawing, is called the wetted canal
cross-section. It also has a trapezium shape and the formula to calculate
its surface area is:
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9. Formula:
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).
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10. Example:
Calculate the surface area of the cross-section and the wetted
cross-section, of the canal shown in next figure.
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Canal cross-section:
base (b) =1.25 m
top line (a) =3.75 m
canal depth (h) = 1.25 m
Formula: A = 0.5 x (b + a) x h
Canal wetted cross-section:
base (b) = 1.25 m
top line (a1) = 3.25 m
water depth (h1) =1.00 m
Formula: A = 0.5 x (b + a1) x h

12. 12
Activity 1: Calculate
the surface area of
the cross-section and
wetted cross-section
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1.
2.

13. 13
Generalization:
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What are the two surface areas of a canal?
Canal cross-section and canal wetted cross-section
What is the formula for canal cross-section?
What is the formula for canal wetted cross-section?
Formula: A = 0.5 x (b + a1) x h
Formula: A = 0.5 x (b + a) x h

14. Activity 2: Calculate the surface area of
the cross-section and wetted cross-section.
(notebook)
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1. Canal cross-section:
b = 3.50 m
a = 4.50 m
h = 2.50 m
Canal wetted cross-section:
b = 3.50 m
a1 = 4.00 m
h1 = 2.00 m
2. Canal cross-section:
b = 4.50 m
a = 4.50 m
h = 3.50 m
Canal wetted cross-section:
b = 4.50 m
a1 = 5.00 m
h1 = 3.00 m
3. Canal cross-section:
b = 5.00 m
a = 7.00 m
h = 4.00 m
Canal wetted cross-section:
b = 5.00 m
a1 = 6.00 m
h1 = 3.00 m
4. Canal cross-section:
b = 10 m
a = 15 m
h = 7 m
Canal wetted cross-section:
b = 10 m
a1 = 13 m
h1 = 5 m
5. Canal cross-section:
b = 15 m
a = 12 m
h = 8 m
Canal wetted cross-section:
b = 15 m
a1 = 10 m
h1 = 6 m

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Determine the following pictures:

17. Determination of the
Surface Area of a
Farm

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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.

19. Field of Regular Shape
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EXAMPLE:
Length of the field =50 m
Width of the field = 30 m
What is the area of the same field, expressed in hectares?
A hectare is equal to 10 000 m. Thus, the formula to
calculate a surface area in hectares is:

20. Field of Irregular Shape
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In this case, the field should be divided in several regular
areas (square, rectangle, triangle, etc.).

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Division of Irregular Field into Regular Areas
Surface area of the square: As = length x width
Surface area of the rectangle: Ar = length x width
Surface area of the triangle: At = 0.5 x base x height
Total surface area of the field: A = As + Ar + At

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