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Area of A Circle: Definition and Examples | EDU.COM

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Area of A Circle: Definition and Examples | EDU.COMEDU.COMResourcesBlogGuidePodcastPlanBackHomesvg]:size-3.5">Math Glossarysvg]:size-3.5">Area of A CircleArea of A Circle: Definition and ExamplesTable of ContentsArea of a Circle Definition of Area of a Circle

The area of a circle is the space occupied by the circle within its boundary (circumference) in a 2D2D2D plane. It is measured in square units and is calculated using the formula A=πr2A = \pi r^2A=πr2, where rrr is the radius of the circle and π\piπ (pi) is a mathematical constant with an approximate value of 3.143.143.14 or 227\frac{22}{7}722​.

A circle is a two-dimensional closed geometric shape consisting of all points at a fixed distance (radius) from a fixed point (center). There are different formulas to find the area of a circle depending on the information available: using radius (A=πr2A = \pi r^2A=πr2), using diameter (A=π4d2A = \frac{\pi}{4} d^2A=4π​d2), or using circumference (A=C24πA = \frac{C^2}{4\pi}A=4πC2​).

Examples of Area of a Circle Example 1: Finding the Area of a Circular Garden Problem:

If the diameter of a circular garden is 505050 feet, find the area of the garden.

Step-by-step solution:

Step 1, Find the radius of the garden using the diameter.

r=d2=502=25r = \frac{d}{2} = \frac{50}{2} = 25r=2d​=250​=25 feet

Step 2, Use the formula for the area of a circle with the radius.

A=πr2A = \pi r^2A=πr2

Step 3, Put the radius value into the formula.

A=π(25)2=625πA = \pi(25)^2 = 625\piA=π(25)2=625π square feet

Step 4, So the area of the circular garden is 625π625\pi625π square feet.

Example 2: Calculating the Area of a Circular Window Problem:

What is the area of a circular window with a diameter of 333 feet?

Step-by-step solution:

Step 1, Find the radius of the window from the diameter.

r=d2=32=1.5r = \frac{d}{2} = \frac{3}{2} = 1.5r=2d​=23​=1.5 feet

Step 2, Apply the area formula using the radius.

A=πr2A = \pi r^2A=πr2

Step 3, Calculate the area by putting the radius value.

A=π×(1.5)2=2.25πA = \pi \times (1.5)^2 = 2.25\piA=π×(1.5)2=2.25π square feet

Step 4, Therefore, the area of the circular window is 2.25π2.25\pi2.25π square feet.

Example 3: Finding the Area of a Circular Table from Circumference Problem:

What is the area of a circular table if it measures 12π12\pi12π feet around its edge?

Step-by-step solution:

Step 1, Identify what we know: the circumference of the table is C=12πC = 12\piC=12π feet.

Step 2, Use the formula to find area when circumference is given:

A=C24πA = \frac{C^2}{4\pi}A=4πC2​

Step 3, Substitute the circumference value into the formula:

A=(12π)24π=144π24πA = \frac{(12\pi)^2}{4\pi} = \frac{144\pi^2}{4\pi}A=4π(12π)2​=4π144π2​

Step 4, Simplify the expression:

A=144π24π=144π4=36A = \frac{144\pi^2}{4\pi} = \frac{144\pi}{4} = 36A=4π144π2​=4144π​=36 square feet

Step 5, The area of the circular table is 363636 square feet.

Comments(4)DDancerOliviaNovember 6, 2025I've used this area of a circle def to help my students. The real-world examples made it easy for them to grasp. Great resource!

TTranslatorIrisNovember 5, 2025This glossary page on the area of a circle is great! It's helped my students grasp the concept easily. Thanks for the clear examples!

YYogiAriaNovember 5, 2025This glossary page is great! I've used it to teach my students the area of a circle. The real-world examples made it much easier for them to grasp.

MCMs. CarterSeptember 17, 2025I’ve used this page to explain the area of a circle to my kids, and the examples really helped them understand it better. Loved the step-by-step solutions—it made math less intimidating!

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