Let's move away from the widely-dreaded two-column proofs that we have been doing in the previous sections, and focus on geometry that revolves solely around computations. In this section, we will use our knowledge of different polygons and circles to help us measure their areas. In the two-dimensional plane, we use area to express a defined quantity of a figure's surface.
We can use various units to describe area. These units of measurement include centimeters, inches, feet, yards, kilometers, miles, and much more. However, because we will be determining the measurements of various figures in two dimensions, we will need to attach a "square", or exponent of 2, to our units. This will signify that we are not talking about a measurement in one direction, but that we are covering a span of squares in two directions. An illustration of the difference between a unit and a unit squared is shown below.
Notice that "3 units" represents a segment of three units, whereas "3 square units" represents an area of (one unit by one unit) squares that is three units long.
The concept of area plays a significant role in all disciplines of mathematics, including algebra and calculus. Therefore, it is one of the most widely-utilized applications in the real world. For instance, we use area when laying down carpet, surveying land, and putting up wallpaper, to name a few examples. You can even use area to help you in an argument with your parents regarding why you shouldn't have to share your small, square bedroom with a sibling! In fact, after studying this section, you will know how to measure the areas of polygons and circles of all sizes.
Main Lesson: Areas of Parallelograms and Triangles
Learn how to measure the areas of parallelograms and triangles by using their area formulas. Also, learn about the relationship these figures have in terms of their areas.
Main Lesson: Areas of Trapezoids
Find out how to use the formula for areas of trapezoids to in order to find the areas of all trapezoids. Also, take a look at an alternate solution of an exercise in which a trapezoid is broken up into smaller shapes.
Main Lesson: Areas of Rhombuses and Kites
Study the area formula for rhombuses and kites. Although one is a parallelogram and the other is not, we will see that they share a common area formula.
Main Lesson: Areas of Circles and Sectors
Our final stop is circles and sectors. Learn how to find the areas of circles and sectors, as well as how their area formulas relate to each other.
Main Lesson: Areas Reference Page
Look at two easy-to-read tables that display the important properties of different figures as well as their area formulas.