The study of geometry includes a set of formulas used to compute the areas of common figures, including triangles, rectangles, parallelograms, trapezoids, and circles. However, each formula only applies when very specific criteria are met. For example, the most common formula used to calculate the area of a triangle, A = (1/2)bh, only applies if you are able to calculate the height of the rectangle—the length of the segment perpendicular to the line containing one side and extending to the opposite vertex.
As trigonometry is primarily focused on the study of triangles—and secondarily on the relationship between triangles and circles—this chapter explores additional formulas that calculate the areas of triangles. It concludes with a set of problems in which you calculate the area of a sector, a roughly triangular region of a circle formed by two radii and an arc of the circle.
This chapter is all about area. Most of it focuses on triangles. By the time you’re done, you’ll be able to calculate the area of a triangle given:
Two angles and one side
Two sides and one angle
The lengths of all three sides
You’ll also calculate the area of sectors, which are sections of a circle that look like pieces of pie. Draw two radii on a circle and then darken in the arc that connects the two points at which those radii touch the circle and you have yourself a sector.