Let’s learn how to determine the area of a circle.
A circle is a shape containing a set of points that are equidistant from a given point. The point is called the center, and the distance from the center to any point in the circle is called the radius.
Twice the length of the radius is called the diameter – it’s the line segment that passes through the center and has its endpoints on the circle itself. So, if you have the radius, you can multiply it by 2 in order to get the diameter,
as represented by the formula, d=2r. Or, if you know the diameter and need the radius, you can divide d by 2, as represented by the expression, r=d/2 . Lastly, the distance around a circle is called the circumference, which is called a perimeter in a polygon.
Related Reading: Perimeter of a Rectangle – Formulas & Examples
The most common units of distance used in a circle are millimeters (mm), centimeters (cm), meters (m), and kilometers (km). The area is the space enclosed inside the circle. It’s measured in square units such as mm2, cm2, m2, and km2. To find the area of a circle, multiply the pi which is approximately 3.14 by the squared radius.
Formula for the Area of a Circle: A = πr2
Example 1: Find the Area of a Circle when given the Radius
Find the area of the circle below.
Solution for Example 1:
Write down the given measurement, which is the radius (r = 10m), and place it in the formula for the area.
Remember that the formula for the area is: A = πr2
Substitute 3.14 for pi and 10m for r.
A = 3.14 (10m)2
Simplify.
A = 3.14 (100m2)
A = 314m2
Therefore, the area of the circle is 314m2.
Example 2: Find the Area of a Circle when given the Diameter
Find the area of the circle below.
Solution for Example 2:
Write down the given measurement, which is the diameter (d = 50m).
Remember that the formula for the area, A = Ï€r2, requires the radius and not the diameter. So, let’s find the radius using the given diameter.
You may recall that the diameter is twice the radius, as represented by the formula, d=2r. Hence, to get the radius, substitute 50m for d.
d = 2r
50m = 2r
Simplify by dividing the equation by 2.
The answer is 25m = r, which is also reflexive to r = 25m.
Therefore, the radius is 25m. Now that we have it, let’s compute the area.
Substitute 3.14 for pi and 25m for r in the formula for the area.
A = πr2
A = 3.14 (25m)2
Simplify.
A = 3.14 (625m2)
A = 1,962.5m2
Therefore, the area of the circle is 1,962.5m2.
Thank you for reading. We hope it’s effective! Always feel free to revisit this page if you ever have any questions about the area of a circle.
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