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2026-01-01
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<p>137 Learners</p>
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<p>Last updated on<strong>September 17, 2025</strong></p>
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<p>Last updated on<strong>September 17, 2025</strong></p>
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<p>The area is the space inside the boundaries of a two-dimensional shape or surface. There are different formulas for finding the area of various shapes/figures. These are widely used in architecture and design. In this section, we will find the area of an arc.</p>
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<p>The area is the space inside the boundaries of a two-dimensional shape or surface. There are different formulas for finding the area of various shapes/figures. These are widely used in architecture and design. In this section, we will find the area of an arc.</p>
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<h2>What is the Area of Arc?</h2>
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<h2>What is the Area of Arc?</h2>
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<p>An arc is a portion<a>of</a>the circumference of a circle. It can be thought of as the 'curved edge' of a sector of the circle. The area of the arc refers to the area of the sector of the circle that the arc is part of.</p>
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<p>An arc is a portion<a>of</a>the circumference of a circle. It can be thought of as the 'curved edge' of a sector of the circle. The area of the arc refers to the area of the sector of the circle that the arc is part of.</p>
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<p>The area of the arc is the total space it encloses.</p>
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<p>The area of the arc is the total space it encloses.</p>
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<h2>Area of the Arc Formula</h2>
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<h2>Area of the Arc Formula</h2>
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<p>To find the area of an arc, we use the<a>formula</a>: (θ/360) × π × r², where θ is the central angle in degrees, and r is the radius of the circle. Now let’s see how the formula is derived. Derivation of the formula: The circle's total area is π × r².</p>
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<p>To find the area of an arc, we use the<a>formula</a>: (θ/360) × π × r², where θ is the central angle in degrees, and r is the radius of the circle. Now let’s see how the formula is derived. Derivation of the formula: The circle's total area is π × r².</p>
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<p>The arc is part of the circle, proportional to the angle θ compared to the full circle of 360 degrees. Thus, the area of the arc (sector) is (θ/360) × π × r². Therefore, the area of the arc = (θ/360) × π × r²</p>
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<p>The arc is part of the circle, proportional to the angle θ compared to the full circle of 360 degrees. Thus, the area of the arc (sector) is (θ/360) × π × r². Therefore, the area of the arc = (θ/360) × π × r²</p>
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<h2>How to Find the Area of Arc?</h2>
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<h2>How to Find the Area of Arc?</h2>
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<p>We can find the area of the arc using this formula, which involves knowing the circle's radius and the central angle. Here’s how:</p>
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<p>We can find the area of the arc using this formula, which involves knowing the circle's radius and the central angle. Here’s how:</p>
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<p>Method Using the Central Angle and Radius If the central angle θ and radius r are given, we find the area of the arc using the formula: Area = (θ/360) × π × r² For example, if θ is 60 degrees and r is 10 cm, what will be the area of the arc? Area = (60/360) × π × 10² = (1/6) × π × 100 ≈ 52.36 cm² The area of the arc is approximately 52.36 cm²</p>
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<p>Method Using the Central Angle and Radius If the central angle θ and radius r are given, we find the area of the arc using the formula: Area = (θ/360) × π × r² For example, if θ is 60 degrees and r is 10 cm, what will be the area of the arc? Area = (60/360) × π × 10² = (1/6) × π × 100 ≈ 52.36 cm² The area of the arc is approximately 52.36 cm²</p>
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<h2>Unit of Area of Arc</h2>
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<h2>Unit of Area of Arc</h2>
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<p>We measure the area of an arc in<a>square</a>units. The<a>measurement</a>depends on the system used:</p>
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<p>We measure the area of an arc in<a>square</a>units. The<a>measurement</a>depends on the system used:</p>
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<p>In the metric system, the area is measured in square meters (m²), square centimeters (cm²), and square millimeters (mm²).</p>
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<p>In the metric system, the area is measured in square meters (m²), square centimeters (cm²), and square millimeters (mm²).</p>
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<p>In the imperial system, the area is measured in square inches (in²), square feet (ft²), and square yards (yd²).</p>
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<p>In the imperial system, the area is measured in square inches (in²), square feet (ft²), and square yards (yd²).</p>
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<h2>Special Cases or Variations for the Area of Arc</h2>
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<h2>Special Cases or Variations for the Area of Arc</h2>
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<p>Since an arc is part of a circle, its area calculation involves the central angle and radius. Here are some special cases:</p>
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<p>Since an arc is part of a circle, its area calculation involves the central angle and radius. Here are some special cases:</p>
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<p><strong>Case 1:</strong>Using the Central Angle and Radius If the central angle and radius are given, use the formula: Area = (θ/360) × π × r².</p>
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<p><strong>Case 1:</strong>Using the Central Angle and Radius If the central angle and radius are given, use the formula: Area = (θ/360) × π × r².</p>
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<p><strong>Case 2:</strong>Using a Full Circle If the arc is a full circle (θ = 360°), the area becomes the area of the circle itself: Area = π × r².</p>
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<p><strong>Case 2:</strong>Using a Full Circle If the arc is a full circle (θ = 360°), the area becomes the area of the circle itself: Area = π × r².</p>
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<h2>Tips and Tricks for Area of Arc</h2>
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<h2>Tips and Tricks for Area of Arc</h2>
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<p>To make sure that you get correct results while calculating the area of an arc, there are some tips and tricks you should know about.</p>
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<p>To make sure that you get correct results while calculating the area of an arc, there are some tips and tricks you should know about.</p>
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<p>Here are some: Ensure the angle θ is in degrees when using the formula. The larger the central angle, the larger the area of the arc. If the angle is given in radians, convert it to degrees by multiplying by (180/π).</p>
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<p>Here are some: Ensure the angle θ is in degrees when using the formula. The larger the central angle, the larger the area of the arc. If the angle is given in radians, convert it to degrees by multiplying by (180/π).</p>
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<h2>Common Mistakes and How to Avoid Them in Area of Arc</h2>
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<h2>Common Mistakes and How to Avoid Them in Area of Arc</h2>
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<p>It is common for people to make mistakes while finding the area of an arc. Let’s take a look at some mistakes made.</p>
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<p>It is common for people to make mistakes while finding the area of an arc. Let’s take a look at some mistakes made.</p>
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<h3>Problem 1</h3>
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<h3>Problem 1</h3>
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<p>The central angle θ of an arc is 90 degrees, and the radius r is 7 m. What will be the area?</p>
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<p>The central angle θ of an arc is 90 degrees, and the radius r is 7 m. What will be the area?</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>We will find the area as 38.48 m²</p>
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<p>We will find the area as 38.48 m²</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Here, the central angle θ is 90 degrees, and the radius r is 7 m.</p>
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<p>Here, the central angle θ is 90 degrees, and the radius r is 7 m.</p>
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<p>The area of the arc = (90/360) × π × 7² = (1/4) × π × 49 ≈ 38.48 m²</p>
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<p>The area of the arc = (90/360) × π × 7² = (1/4) × π × 49 ≈ 38.48 m²</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 2</h3>
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<h3>Problem 2</h3>
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<p>What will be the area of the arc if the central angle is 120 degrees and the radius is 5 cm?</p>
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<p>What will be the area of the arc if the central angle is 120 degrees and the radius is 5 cm?</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>We will find the area as 26.18 cm²</p>
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<p>We will find the area as 26.18 cm²</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>If the central angle is 120 degrees and the radius is 5 cm, we use the formula:</p>
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<p>If the central angle is 120 degrees and the radius is 5 cm, we use the formula:</p>
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<p>Area = (120/360) × π × 5² = (1/3) × π × 25 ≈ 26.18 cm²</p>
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<p>Area = (120/360) × π × 5² = (1/3) × π × 25 ≈ 26.18 cm²</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 3</h3>
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<h3>Problem 3</h3>
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<p>The area of an arc is 78.54 m² and the radius is 10 m. Find the central angle.</p>
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<p>The area of an arc is 78.54 m² and the radius is 10 m. Find the central angle.</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>We find the central angle θ as 90 degrees</p>
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<p>We find the central angle θ as 90 degrees</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>To find the central angle, use the formula:</p>
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<p>To find the central angle, use the formula:</p>
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<p>Area = (θ/360) × π × 10².</p>
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<p>Area = (θ/360) × π × 10².</p>
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<p>Here, the area is 78.54 m², and the radius is 10 m: 78.54 = (θ/360) × π × 100 θ = (78.54 × 360)/(π × 100) θ ≈ 90 degrees</p>
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<p>Here, the area is 78.54 m², and the radius is 10 m: 78.54 = (θ/360) × π × 100 θ = (78.54 × 360)/(π × 100) θ ≈ 90 degrees</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h2>FAQs on Area of Arc</h2>
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<h2>FAQs on Area of Arc</h2>
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<h3>1.Is it possible for the area of the arc to be negative?</h3>
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<h3>1.Is it possible for the area of the arc to be negative?</h3>
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<p>No, the area of the arc can never be negative. The area of any shape will always be positive.</p>
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<p>No, the area of the arc can never be negative. The area of any shape will always be positive.</p>
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<h3>2.How to find the area of an arc if the central angle and radius are given?</h3>
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<h3>2.How to find the area of an arc if the central angle and radius are given?</h3>
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<p>If the central angle and radius are given, find the area using the formula: Area = (θ/360) × π × r².</p>
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<p>If the central angle and radius are given, find the area using the formula: Area = (θ/360) × π × r².</p>
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<h3>3.What if the central angle is given in radians?</h3>
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<h3>3.What if the central angle is given in radians?</h3>
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<p>If the central angle is in radians, convert it to degrees by multiplying by (180/π) before using the formula.</p>
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<p>If the central angle is in radians, convert it to degrees by multiplying by (180/π) before using the formula.</p>
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<h3>4.What is meant by the area of the arc?</h3>
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<h3>4.What is meant by the area of the arc?</h3>
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<p>The area of the arc is the total space occupied by the sector of the circle that the arc is part of.</p>
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<p>The area of the arc is the total space occupied by the sector of the circle that the arc is part of.</p>
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<h2>Seyed Ali Fathima S</h2>
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<h2>Seyed Ali Fathima S</h2>
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<h3>About the Author</h3>
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<h3>About the Author</h3>
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<p>Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.</p>
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<p>Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.</p>
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<h3>Fun Fact</h3>
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<h3>Fun Fact</h3>
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<p>: She has songs for each table which helps her to remember the tables</p>
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<p>: She has songs for each table which helps her to remember the tables</p>