Unit 9: Perimeter and Area
Calculating area and perimeter are probably the two most common applications of geometry.
For example, if you want to install some carpet you need to measure the size of your space so you know how much carpet you need to buy to cover it (in terms of square feet or square meters). To install a fence, you need to calculate the perimeter of your yard so you know how much lumber you need to buy. To wire a room you need to calculate the perimeter of your room's interior walls so you know how much cable you need to buy and how much your labor and installation will cost (your electrician will likely charge you by the foot).
Completing this unit should take you approximately 5 hours.
9.1: Perimeter and Area Basics
Your first step in this unit is to understand the basic idea of perimeter, area, and the language mathematicians commonly use in these types of problems.
9.2: Area of Triangles
Let's look at how to calculate the area and perimeter of the different types of geometric shapes we have studied in this course. It may be helpful to keep a list of the different area formulas you encounter in this unit. First, we'll look at triangles.
9.3: Area and Perimeter of Rectangles and Squares
Now, let's look at the area and perimeter formulas of rectangles and squares.
9.4: Area of a Parallelogram
The next shape we study is the parallelogram. When you calculate the area of a parallelogram, envision rearranging it into a rectangle, and use the formulas you have just learned.
9.5: Area and Perimeter of Trapezoids
Now, let's look at trapezoids.
9.6: Area and Perimeter of Rhombuses and Kites
Next, we focus on rhombuses and kites.
9.7: Area and Perimeter of Similar Polygons
Here, we explore how to determine the area and perimeter of similar polygons. Similar polygons have identical angles and proportional side lengths.
When studying circles, we use the term circumference to describe the distance around the circle.
9.9: Arc Length
The arc length is the length of circumference in a "slice" of a circle defined by an arc.
9.10: Area of a Circle
We can now determine the area of a circle. The area of a circle is pi times the radius squared (A = π r²).
Pi is a number – approximately 3.142. It is the circumference of any circle divided by its diameter. The number pi, denoted by the Greek letter π (pronounced "pie"), is one of the most common constants in all of mathematics.
9.11: Area of Composite Shapes
Lastly, we learn about composite shapes, which are non-standard polygons.