How do you find the area of a circle?

Category: 2D Shapes »

Course: Geometry »

Relevant MM Lessons:
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Circle Area Concept and Formula

In order to find the area of a circle, you need to know its radius - the distance measured from the center to the edge. With a given radius $r$, the area of a circle is:$$A = \pi r^2$$Let's see a quick example.In the above diagram, we are given that the radius of the circle is $3$. Therefore, the area of the circle is:$$A = \pi r^2 = \pi (3)^2$$$$ = 9\pi$$One way a quiz might try to trick you is to give you the diameter instead. You cannot easily use the diameter to calculate area without making an error. You should always pay attention to what you are given, and if you are given a diameter, cut it in half to get the radius (the relationship between diameter and radius is $d = 2r$).Example:This time we are given a circle with a diameter of $8$. Since $d = 2r$, this implies that $r = 4$. Now that we know the radius, we can proceed with the area calculation. Do not erroneously use the diameter in the formula and then cut your answer in half! That doesn't work!$$d = 8 \rightarrow r = 4$$$$A = \pi r^2 = \pi (4)^2$$$$ = 16\pi$$