Performing Mensuration and Calculation

Module Title: Performing Mensuration and Calculation

HOW TO USE THIS MODULE

Activities are properly arranged in this module to help you work at your own pace, this module also covers the knowledge, skills, and proper attitudes you need in Drafting Technology.

A pre-assessment precedes the learning activities in each module to determine your level and need.
The learning activity page gives the sequence of the learning task. This page serves as the road map in achieving the desired objectives.

After you accomplished all the tasks required, a post-assessment is given to check if you are already competent with the specified learning outcome/s and are ready for the next task.

Definitions of terms are provided in this module for your better understanding.

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.

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

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.

Common 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.

Common 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 

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

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

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 Geometric Solid