This Crash Course is a review of several geometry topics from Secondary 1 and 2. To understand these two videos, you'll need to know the following: the difference between the perimeter and area of a plane figure, the perimeter and area formulas for all plane figures, the proportion used to calculate the measure of a circular arc, the proportion used to calculate the area of a circle sector, and how to convert units of length and units of area.
When you're faced with a problem that involves plane figures, consider the following to help you before you calculate:
-
Determine if it is a perimeter problem or an area problem.
-
Convert all dimensions to the same units of measure.
-
Draw a diagram of the situation and enter any information about the problem.
-
Make a plan of the steps to take to solve the problem.
The following table helps determine if it is a perimeter problem or an area problem.
|
Perimeter |
Area |
|---|---|
|
Synonyms |
|
|
|
|
Examples |
|
|
|
|
Units |
|
|
|
There are 2 ways to calculate the area of a decomposable figure:
-
Calculate the area of the whole figure and subtract the area of the parts that need to be removed.
-
Start by breaking down your decomposable figure into simpler shapes, such as triangles, rectangles and so on. Then calculate the area of each of the parts, and add them together.
Here are the conversion tables for units of length and area:
Here are the formulas for the perimeter and area of plane figures:
Use one of the following 2 proportions to calculate the measure of a circular arc or the area of a circle sector:||\dfrac{\text{Central angle}}{360^\circ}=\dfrac{\text{Arc measurement}}{\text{Circumference}}||or||\begin{align}\frac{\text{Central angle}}{360^{\circ}}&=\frac{\text{Area of sector}}{\text{Area of circle}}\end{align}||