Program/Course : DRAFTING TECHNOLOGY

Unit of Competency : PERFORM MENSURATION AND

CALCULATION

Module Title : Performing Mensuration and

Calculation

INTRODUCTION

This module is designed to familiarize students with mensuration

and calculation. A description of shape is valueless without proper
and complete indication of size. The shop worker preferably the
draftsman must know the exact width, height and depth of a work
piece, as well as the diameter and precise location of holes.
Accuracy of measurements depends on one's ability to use
measuring tools correctly.
Proper practice in holding different tools, instruments and
materials as well as safety measures are also included in this
module.

SUMMARY OF LEARNING OUTCOMES

Upon the completion of this module, you should be able to:

LO1. Select measuring instruments; and

LO2. Carry out measurements and calculation

 TECHNICAL TERMS

Aligned system is a dimensioning system where all dimensions are

parallel to the line being measured.
Angle is a geometrical figure composed of two straight lines
intersecting at one of their extremities.
Circle is a closed curvewhere all points are equally distant from the
center.
Concentric circles consist of two or more circles with a common
center.
Cone is generated by a straight line moving in contact with a
curved line in passing through a fixed point.
Dodecahedron is a solid shape with twelve pentagons.
Eccentric circles are circles having no common center.
Heptagon is a polygon with seven sides.
Hexahedron is a solid cube.
Hexagon is a polygon with six sides.
Icosahedron is a solid shape with twenty triangles.
Nonagon is a polygon with seven sides.
Octagon is a polygon with eight sides.
Octahedron is a solid shape with eight triangles.
Pentagon is a polygon with five sides.
Polygon is a plane geometric figure bounded by straight lines.
Prism has two bases which are parallel equal polygon.
Pyramid has a polygon for a base and triangular lateral faces
intersecting at a common point called vertex.
Quadrilateral is a four-sided plane geometrical figure.
Radius is the length of a straight line connecting the center of a
circle with a point on the circumference of a circle.
Sector is a portion of a circle bounded by two radii and the
intercepted arc.
Segment is a portion of a circle bounded by an arc and a chord.
Solid is a three-dimensional figure.
Sphere is generated by a circle revolving around each diameter.
Tetrahedron is a solid with four triangles.

Program/Course : DRAFTING TECHNOLOGY

Unit of Competency : PERFORM MENSURATION AND

CALCULATION

Module Title : Performing Mensuration and

Calculation

Nominal Duration : 20 hours

Learning Outcome 1 : Select measuring instruments

Assessment Criteria
1. Objects or components to be measured are identified,
classified and interpreted according to appropriate regular
geometric shape.
2. Measuring tools are selected/identified as per object to be
measured per job requirements.
3. Correct specifications are obtained from relevant sources.
4. Measuring instruments are selected according to job
requirements.
5. Alternative measuring tools are used without sacrificing
cost and quality of work.
6. Measurements are obtained according to job requirements.

References:
Giesecke, Mitchell and Spencer. Technical Drawing; The Macmillan
Company: 1999.
French and Vierck. Engineering Drawing 10th edition MacGraw, Hill Book
Company, 1960

German M. Manaois. Drafting 1 and 2 Phoenix Publishing:1983

Norman Stirling. Introduction to Technical Drawing Delmar Publishing:

1977

Competency Based Learning Material, Civil Technology

LEARNING EXPERIENCES / ACTIVITIES

Learning Outcome # 1: Select measuring instruments

Learning Activities Special Instruction

 1. Read Information Sheet No. 1
on geometric figures.

2. Answer Self Check No. 1.1  Try to answer Self Check No. 1.1.

3. Check your answers using the

answer key.

4. Read Information Sheet No. 2

about measuring tools.

5. Perform task on Self Check No.  Try to perform the said task.
2.1  Ask your teacher on the items
which are difficult to perform.

6. Read Information Sheet No. 3

on formulas for computing
volume, area and perimeter of
a plane and geometric figures.

7. Answer Self Check No. 3.1  Try to answer Self Check No. 3.1

INFORMATION SHEET # 1

LO1. Select measuring instruments

GEOMETRIC FIGURES

The geometric figures commonly used in drawing pictures are

lines, angles, triangles, quadrilaterals, regular polygons, circles and
arcs and solids.
LINE. A line is a set of points. A portion of the line between two
distinct points is a called a line segment. The following are the
different kinds of lines.
1. Straight line. It is the shortest distance between two
points.
2. Parallel lines. These are lines on the same plane which
will not meet no matter how long you extend them.
3. Perpendicular lines. These are two intersecting lines which
form right angles.

STRAIGHT LINES
PARALLELL LINES

PERPENDICULAR
LINES

ANGLE. An angle is a figure formed by two rays with common end

point. Angles are classified according to their measures. The
following are the different kinds of angles.
1. Straight angle. It is an angle whose measure is 1800.
2. Right angle. It is an angle whose measure is 900.

3 Acute angle. It is an angle whose measure is less than

900.
4. Obtuse angle. It is an angle whose measure is more than
900 but less than 1800.
5. Complementary angles. These are two angles whose
sum measures 900.
 6. Supplementary angles. These are two angles whose
sum measures 1800.

1800
A 900
LESS THAN 900
B

STRAIGHT ANGLE RIGHT ANGLE ACUTE ANGLE

1800 900
MORE THAN 900 A
A
B B

OBTUSE ANGLE COMPLEMENTARY ANGLES

SUPPLEMENTARY ANGLES

POLYGON. A polygon is a closed figure formed by line segments

intersecting at end points. The line segments are called sides of the
polygon. Polygon is classified according to the number of sides. The
following are the different kinds of polygon.

1. Triangle. It is a three-sided polygon. The different kinds of

triangles are as follows:
a. Equilateral has all three sides equal.
b. Isosceles has two of the sides equal.
c. Scalene- has three sides of unequal length.
d. Right is where one of the angles is a right angle
 QUADRILATERALS AND TRIANGLES

RECTANGLE SQUARE RHOMBUS

TRAPEZOID TRAPEZIUM ISOSCELES TRIANGLE RIGHT EQUILATERAL TRIANGLE

TRIANGLE

2. Quadrilateral. It is a four sided polygon. The different kinds of

quadrilaterals are as follows:
a. Parallelogram is a quadrilateral with two pairs of opposite
sides parallel and equal.
b. Rectangle is a parallelogram with a right angle.
c. Square is a rectangle with four equal sides.
d. Rhombus is a parallelogram with a right.
e. Trapezoid is a quadrilateral with one pair of opposite sides
parallel in which one of them is longer than the other.
f. Isosceles trapezoid is a trapezoid with its nonparallel
sides equal.
g. Trapezium is a quadrilateral with no parallel sides and no
equal angles.
3. Pentagon. It is a five-sided polygon. If all the sides and angles of
the pentagon are equal, it is a regular pentagon. The measure of
each included angle is 1080.
4. Hexagon. It is polygon with six sides. If all the sides and angles
are equal, it is a regular hexagon. The measure of each included
angle of a regular hexagon is1200.
5. Heptagon. It is a polygon with seven sides. If all the sides and
angles are equal, it is a regular heptagon and the measure of each
angle is approximately equal to 128.560.
6. Octagon. It is a polygon with eight sides. If all the sides and
angles are equal, it is a regular octagon and the measure of each
angle is 1350.
7. Nonagon. It is a polygon with nine sides. If all the sides and
angles are equal, it is a regular nonagon and the measure of each
angle is 1400.
8. Decagon. It is a polygon with ten sides. If all the sides and
angles are equal, it is a regular decagon and the measure of each
angle is 1440.

REGULAR POLYGONS

PENTAGON OCTAGON
HEXAGON

EQUILATERAL
TRIANGLE SQUARE

CIRCLE. A circle is a closed curve, all points are equally distant

from the center. An arc is a portion of the circumference of the
circle. The following are terms related to a circle or parts of a circle.
1. Concentric circles consist of two or more circles with a
2. Eccentric circles are circles having no common center.
3. Ellipse is an oblique circle with two axes, the minor axis and
the major axis.
4. Radius is a line segment from the center to any point on the
circle.
5. Chord is a line segment whose endpoints lie on the circle.
 6. Diameter is a chord that passes through the center.
7. Sector is a portion of a circle bounded by two radii and the
intercepted arc.
8. Segment is a portion of a circle bounded by an arc and a
chord.
9. Circumference is the distance around the circle. The
circumference is equal to the diameter multiplied by 3.1416.
10. Quadrant is one-fourth of the entire area of the circle.

KINDS AND PARTS OF CIRCLE

CIRCUMFERENCE
ANGLES

TANGENT

RADIUS
CHORD
QUADRANT
900
CENTER RADIUS

ARC

SEGMENT
SECTOR
DIAMETER

CONCENTRIC CIRCLES ECCENTRIC CIRCLES

SOLID. A solid is a three-dimensional figure. The three dimensions

are the length, width and height. The following are the different
kinds of solids.
1. Sphere is a three dimensional figure whose points are
located at a constant distance away from the center.
2. Prism is a three dimensional figure with a polygonal base
and triangular lateral faces.
3. Cube is a prism whose faces are congruent squares. An
example of a cube is a dice.
4. Cylinder is a solid figure with two circular bases in parallel
plane and parallel line segments connecting to these bases. An
example of a cylinder is a tin can.
5. Cone is solid figure with a circular base and a surface formed
by line segments joining every point on the edge of the base to
a common point in a parallel plane.
6. Tetrahedron is a solid figure composed of four equilateral
triangles.
7. Dodecahedron is a solid figure bounded by twelve equal
regular pentagons.
8. Icosahedron is a solid figure bounded by twenty equilateral
triangles.

COMMON GOEMETRIC SOLIDS

CYLINDER TETRAHEDRON HEXAHEDRON OCTAHEDRON OCTAHEDRON

PRISM

SPHERE DODECAHEDRON ICOSAHEDRON CONE PYRAMID