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Areas using coordinates
Sometimes you can find areas using coordinates, possibly with the help of tools like the distance formula or equations of perpendicular lines.
(Fancier formulas like the shoelace formula can also help, if you like that kind of thing.)
Areas using trigonometry
You may also find trig helpful when given angle information. For example, trig lets you easily find the area of a triangle in terms of two sides and the angle between them.