Lesson 5 Perform Mensuration and Calculation

LESSON 5: PERFORM MENSURATION AND
CALCULATION
ILLUSTRATION 7

DIFFERENT MEASURING TOOLS AND THEIR PROPER
HANDLING
LO 1. Select measuring instruments

RULER
Ruler is the most popular type of measuring tool. It is
usually 6 or 12 inches in length. It is needed for
measuring sizes and distances.

RULER
How to use a ruler? Check this out!
How to read a ruler? Check this out!
https://www.wikihow.com/Use-a-Ruler
https://www.wikihow.com/Read-a-Ruler
How to measure inches and centimeters using a ruler? Check this out!
https://www.youtube.com/watch?v=VzW2sdCe228
https://www.youtube.com/watch?v=tuBLuIW1U70
Inches:
Centimeters:

RULER
Ruler measurements in inches: Ruler measurements in centimeters:

TRIANGLES
Triangles are used for drawing vertical and oblique lines.
The most commonly used triangles are the 45˚ and the 30
˚ x 60 ˚.

TRIANGLES
How to use a triangle? Check this out!
https://www.youtube.com/watch?v=JKmDy9hXI-4

PROTRACTOR
Protractor is used for measuring and setting of angles
other than those obtainable with the triangles.

PROTRACTOR
Different kinds of angles can be measured and drawn using a protractor.

PROTRACTOR
How to use a protractor? Check this out!
https://www.wikihow.com/Use-a-Protractor
https://www.helpingwithmath.com/by_subject/geometry/geo_protractor_4md6.htm

COMPASS
Compass is used to draw circles, arcs, radii, and parts of
many symbols.

COMPASS
How to use a compass? Check this out!
https://www.youtube.com/watch?v=02XRad7s1Io

DIVIDER
Divider is similar to the compass in construction. As the
name implies, divider is used for dividing distances into a
number of equal parts by the trial-and-error method.

DIVIDER
Steps in Using a Divider
a. Align each arm of the dividers so that one point is laying on the
start point of the measurement you want to transfer and the
other divider point is laying on the endpoint of that same
measurement.
b. Lift the dividers off the measurement you intend to transfer,
being careful not to change their alignment.
c. Place the dividers over the location you'd like to transfer the
measurement to, and make a pencil mark to indicate where each
of the dividers' pointers sits. This duplicates the measurement.

DIVIDER
How to use a divider? Check this out!
https://www.youtube.com/watch?v=FElfUoNcK6o

TRADE MATHEMATICS/MENSURATION
LO 2. Carry out mensuration and calculation

PROPORTION AND
SCALE IN ART
Proportion and scale are principles of art that describe the size, location, or
amount of one element in relation to another. They have a great deal to do with the
overall harmony of an individual piece and our perception of the art.
Scale is used in art to describe the size of one object in relation to
another, each object is often referred to as a whole.
Proportion has a very similar definition but tends to refer to the
relative size of parts within a whole. In this case, the whole can be a
single object like a person's face or the entire artwork as in
a landscape.

PROPORTION AND
SCALE IN ART
Examples of SCALE:
1:10
1/4 in. = 1 ft.
1-to-1
full-size
life-size
monumental

PROPORTION AND
SCALE IN ART
SCALE DRAWING
A drawing that shows a real object
with accurate sizes reduced or enlarged by
a certain amount (called the scale).
The scale is shown as the length in the
drawing, then a colon (":"), then the matching
length on the real thing.
Example: This drawing has a scale of "1:10", so anything
drawn with the size of "1" would have a size of "10" in
the real world, so a measurement of 150mm on the
drawing would be 1500mm on the real horse.

PROPORTION AND
SCALE IN ART
SCALE: Sample Problems
1. Dimensions of a house are 300 feet by 125 feet. If 1 inch represents 50
feet, what are the dimensions of the house on the drawing?
Answer: 15 and 16.25
2. If 1 inch represents 65 miles on a map, then how many inches will
represent 2300 miles?
Answer: 10

MEASUREMENTS
The measurements of different types of objects are taken in different ways. For works such as
engravings, the dimensions of both the printing plate and the sheet may be significant. Some works,
such as costume, may be identified by size, while others, such as examples of graphic design, are
identified by format. For a video or film, technical formats and running time are the customary way of
identifying size and shape.
Measurements help to identify an object. They also make it possible to distinguish between
otherwise similar works, and to group comparable objects according to shared characteristics.
Measurements can be taken with the aid of precise instruments, and therefore are very accurate.
They can also be estimations, taken on the basis of "sight," or historical assessments of uncertain
accuracy.

MEASUREMENTS - DIMENSIONS
Dimensions in mathematics are the measure of the size or distance of
an object or region or space in one direction. In simpler terms, it is the
measurement of the length, width, and height of anything.

Zero Dimensional One Dimensional
A point is a zero-dimensional object as it
has NO length, width or height. It has no
size. It tells about the location only.
A line segment drawn on a surface
is a one-dimensional object, as it
has only length and no width.

Two Dimensional (2D) Three Dimensional (3D)
The two dimensions are
height and width.
The three dimensions are height
and width and depth. Depth is
often applied by projecting a
shadow.

3-Dimensional

TYPE UNIT
The kind of dimension taken of a particular area
or part of an object or work.
The unit of measurement used.
height
width
depth
length
circumference
diameter
volume
weight
area
inches
centimeters
millimeters
meters
feet
cubic centimeters
square feet

ENGLISH AND METRIC SYSTEM OF
UNITS FOR MEASUREMENT
There are two systems of measurement: the English system which originated
in England and the Metric system or Systems International (S.I) which originated
in France.
The basic unit in the Systems International measurement is called the meter.
The meter is divided into 100 centimeters. Each centimeter is divided into 10
millimeters. They are abbreviated as follows:
Millimeters mm
Centimeters cm
Decimeters dm
Meters m

Metric System of Measurement (linear equivalent)
10 millimeters (mm.) = 1 centimeter (cm.)
10 centimeters (cm.) = 1 decimeter (dm.)
10 decimeter (dm.) = 1 meter (m.)
10 meters (m.) = 1 decameter (Dm.)
10 decameter (Dm.) = 1 hectometer (Hm.)
10 hectometer (Hm.) = 1 kilometer (Km.)
10 kilometer (Km.) = 1 mayriameter (Mn.)
English System of Measurement (linear equivalent)
12 inches (in.) = 1 foot (ft.)
3 feet (ft.) = 1 yard (yd.)

Metric Conversion Table
1 millimeter = 0.03937 inches (in.)
1 centimeter = .3937 inches (in.)
1 meter = 39.37 inches (in.)
English Conversion Table
1 inch (in.) = .0254 mm. = 2.54 cm. = .0254 (m.)
1 foot (ft.) = 304.8 mm. = 30.48 cm = .3048 (m.)
1 yard (yd.) = 914.4 mm = 91.4 cm = .9144 (m.)

Conversion Formulas
Length in inches x 0.0254 = length in meters
Length in inches x 2.54 = length in centimeters
Length in feet ÷ 3.28 = length in meters
Length in meters x 39.37 = length in inches
Length in inches ÷ 39.37 = length in meters
Length in feet x 0.305 = length in meters
Length in feet x 30.5 = length in centimeters

FRACTIONS, PERCENTAGE AND
DECIMALS
Decimals, Fractions and Percentages are just different ways of showing the same value:

DECIMALS
Example values: Percent Decimal Fraction
1% 0.01 1/100
5% 0.05 1/20
10% 0.1 1/10
12½% 0.125 1/8
20% 0.2 1/5
25% 0.25 1/4
331/3% 0.333... 1/3
50% 0.5 1/2
75% 0.75 3/4
80% 0.8 4/5
90% 0.9 9/10
99% 0.99 99/100
100% 1
125% 1.25 5/4
150% 1.5 3/2
200% 2

DECIMALS
Let’s convert from PERCENT to DECIMAL
To convert from percent to decimal: divide by 100, and remove the "%" sign.
The easiest way to divide by 100 is to move the decimal point 2 places to the
left:

DECIMALS
Let’s convert from DECIMAL to PERCENT
To convert from decimal to percent: multiply by 100, and add a "%" sign.
The easiest way to multiply by 100 is to move the decimal point 2 places to
the right:

DECIMALS
Let’s convert from FRACTION to DECIMAL
The easiest way to convert a fraction to a decimal is to divide the top number
by the bottom number (divide the numerator by the denominator in
mathematical language).

DECIMALS
Let’s convert from DECIMAL to FRACTION

DECIMALS
Let’s convert from FRACTION to PERCENTAGE
The easiest way to convert a fraction to a percentage is to divide the top
number by the bottom number. then multiply the result by 100, and add the
"%" sign.

DECIMALS
Let’s convert from PERCENTAGE to FRACTION
To convert a percentage
to a fraction, first convert
to a decimal (divide by
100), then use the steps
for converting decimal to
fractions.

Sources:
https://en.wikibooks.org/wiki/Elements_of_Art/Two_and_Three_Dimensions
http://besser.tsoa.nyu.edu/impact/f95/Cdwa/MEASURE.HTML
https://www.splashlearn.com/math-vocabulary/geometry/dimensions
https://www.frameiteasy.com/learn/how-to-measure-art-framing/
https://www.mathsisfun.com/decimal-fraction-percentage.html

Lesson 5 Perform Mensuration and Calculation

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