7 Geometry
Section Information
Outcome/Competency: You will be able to model and calculate scenarios in two- and three-dimensions using geometry.
Timing: 26h
Rationale: Why is it important for you to learn this skill?
Geometry is the study of shapes. Being able to calculate volume and area of a shape, for example, is very important in calculating supplies required for building.
Objectives:
To be competent in this area, the individual must be able to:
- Demonstrate understanding of perimeter, area of 2-D shapes, and surface area and volume of 3-D objects including units in SI and Imperial systems of measurement
Learning Goals
- Model, calculate, interpret, and solve problems in two and three dimensions by using different representations and manipulating formulae
- Apply conversion factors using unit analysis and calculation to solve scenarios and situational problems
Introduction:
In this section you will learn about circumference, diameter, radius, area, surface area, and volume. You’ll be presented with concepts and examples, and given opportunities to practice throughout.
Chapter Contents:
- Topic 1: Perimeter and Circumference
- Topic 2: Area
- Topic 3: Surface Area
- Topic 4: Volume
- Test: Outcome 7
Topic 1: Perimeter and Circumference
We can make use of conversion skills with denominate numbers to make measurements of geometric figures such as rectangles, triangles, and circles. To make these measurements we need to be familiar with several definitions.
1.1 Polygons
A polygon is a closed plane (flat) figure whose sides are line segments (portions of straight lines).
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Polygons |
Not polygons |
1.2 Perimeter
The perimeter of a polygon is the distance around the polygon. To find the perimeter of a polygon, we simply add up the lengths of all the sides.
Example 1
Don’t be tempted to memorize a formula for this. Some people may think that they should memorize a formula such as: Perimeter = 2X length + 2 X width. This type of memorization is unnecessary if you simply remember the perimeter is the sum of all the sides.
Example 2
The sides do not need to be going perpendicular or parallel to each other. In this irregular shape, to find the perimeter, you still need to add all the sides.
Example 3
In some regular shapes you will need to figure out unknown measurements based on other given measurements. Find the sides labeled A, B and C.
If the measurements you need are across the shape, it is sometimes useful to visualize them all together like in this diagram:
Consider side A:
The unknown top side, A (blue), is 10 cm long.
Consider side B:
The unknown side B (yellow), is 8 cm.
Consider unknown side C:
The unknown side, C (blue), is 11 cm long.
1.3 Circumference/Diameter/Radius
Circumference
The circumference of a circle is the distance around the circle. In plain language, the circumference is the perimeter of a circle.
You could measure the circumference of a circle with a string, but if you wanted to calculate the circumference, you need to use