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2026-01-01
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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>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 the octagon.</p>
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<p>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 the octagon.</p>
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<h2>What is the Area of an Octagon?</h2>
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<h2>What is the Area of an Octagon?</h2>
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<p>An octagon is a polygon with eight sides and eight angles. A regular octagon has all sides of equal length and all interior angles are equal. The area of the octagon is the total space it encloses.</p>
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<p>An octagon is a polygon with eight sides and eight angles. A regular octagon has all sides of equal length and all interior angles are equal. The area of the octagon is the total space it encloses.</p>
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<h2>Area of the Octagon Formula</h2>
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<h2>Area of the Octagon Formula</h2>
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<p>To find the area of a regular octagon, we use the<a>formula</a>: Area = 2 × (1 + √2) × a², where 'a' is the length of a side. Let's understand how this formula is derived.</p>
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<p>To find the area of a regular octagon, we use the<a>formula</a>: Area = 2 × (1 + √2) × a², where 'a' is the length of a side. Let's understand how this formula is derived.</p>
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<p>Derivation of the formula: A regular octagon can be divided into 8 isosceles triangles by drawing lines from the center to each vertex. For one triangle, the<a>base</a>is the side 'a' of the octagon, and the height can be found using<a>trigonometry</a>. The area of one triangle is (1/2) × base × height. The total area of the octagon is 8 times the area of one triangle, which simplifies to 2 × (1 + √2) × a².</p>
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<p>Derivation of the formula: A regular octagon can be divided into 8 isosceles triangles by drawing lines from the center to each vertex. For one triangle, the<a>base</a>is the side 'a' of the octagon, and the height can be found using<a>trigonometry</a>. The area of one triangle is (1/2) × base × height. The total area of the octagon is 8 times the area of one triangle, which simplifies to 2 × (1 + √2) × a².</p>
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<h2>How to Find the Area of an Octagon?</h2>
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<h2>How to Find the Area of an Octagon?</h2>
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<p>The area of a regular octagon can be found using the side length. Here’s the method: Method Using the Side Length If the side length 'a' is given, use the formula Area = 2 × (1 + √2) × a².</p>
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<p>The area of a regular octagon can be found using the side length. Here’s the method: Method Using the Side Length If the side length 'a' is given, use the formula Area = 2 × (1 + √2) × a².</p>
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<p>For example, if the side length is 5 cm, what will be the area of the octagon? Area = 2 × (1 + √2) × 5² = 2 × (1 + √2) × 25 = 2 × (1 + 1.414) × 25 = 2 × 2.414 × 25 = 120.7 cm² The area of the octagon is approximately 120.7 cm².</p>
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<p>For example, if the side length is 5 cm, what will be the area of the octagon? Area = 2 × (1 + √2) × 5² = 2 × (1 + √2) × 25 = 2 × (1 + 1.414) × 25 = 2 × 2.414 × 25 = 120.7 cm² The area of the octagon is approximately 120.7 cm².</p>
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<h2>Unit of Area of Octagon</h2>
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<h2>Unit of Area of Octagon</h2>
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<p>We measure the area of an octagon in<a>square</a>units. The<a>measurement</a>depends on the system used: 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>We measure the area of an octagon in<a>square</a>units. The<a>measurement</a>depends on the system used: 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 Octagon</h2>
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<h2>Special Cases or Variations for the Area of Octagon</h2>
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<p>A regular octagon has equal sides and equal angles, making the formula for its area consistent. However, for irregular octagons, different methods may be required:</p>
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<p>A regular octagon has equal sides and equal angles, making the formula for its area consistent. However, for irregular octagons, different methods may be required:</p>
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<p><strong>Case 1:</strong>Regular Octagon Use the formula Area = 2 × (1 + √2) × a², where 'a' is the side length.</p>
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<p><strong>Case 1:</strong>Regular Octagon Use the formula Area = 2 × (1 + √2) × a², where 'a' is the side length.</p>
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<p><strong>Case 2:</strong>Irregular Octagon An irregular octagon requires dividing it into known shapes, such as triangles or rectangles, and summing their areas.</p>
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<p><strong>Case 2:</strong>Irregular Octagon An irregular octagon requires dividing it into known shapes, such as triangles or rectangles, and summing their areas.</p>
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<h2>Tips and Tricks for Area of Octagon</h2>
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<h2>Tips and Tricks for Area of Octagon</h2>
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<p>To ensure correct results while calculating the area of an octagon, consider these tips and tricks:</p>
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<p>To ensure correct results while calculating the area of an octagon, consider these tips and tricks:</p>
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<ul><li>Ensure all sides are equal for a regular octagon. </li>
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<ul><li>Ensure all sides are equal for a regular octagon. </li>
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<li>Use trigonometry for height if calculating manually. </li>
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<li>Use trigonometry for height if calculating manually. </li>
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<li>For irregular octagons, divide into simpler shapes.</li>
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<li>For irregular octagons, divide into simpler shapes.</li>
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</ul><h2>Common Mistakes and How to Avoid Them in Area of Octagon</h2>
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</ul><h2>Common Mistakes and How to Avoid Them in Area of Octagon</h2>
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<p>It is common for individuals to make mistakes while finding the area of an octagon. Here are some common mistakes:</p>
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<p>It is common for individuals to make mistakes while finding the area of an octagon. Here are some common mistakes:</p>
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<h3>Problem 1</h3>
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<h3>Problem 1</h3>
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<p>The side length of a regular octagon-shaped tile is given as 12 cm. What will be the area?</p>
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<p>The side length of a regular octagon-shaped tile is given as 12 cm. 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>The area is approximately 695.4 cm².</p>
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<p>The area is approximately 695.4 cm².</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Here, the side length 'a' is 12 cm.</p>
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<p>Here, the side length 'a' is 12 cm.</p>
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<p>The area of the octagon = 2 × (1 + √2) × a² = 2 × (1 + √2) × 12² = 2 × 2.414 × 144 = 695.4 cm².</p>
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<p>The area of the octagon = 2 × (1 + √2) × a² = 2 × (1 + √2) × 12² = 2 × 2.414 × 144 = 695.4 cm².</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 a regular octagon if the side length is 7 m?</p>
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<p>What will be the area of a regular octagon if the side length is 7 m?</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>The area is approximately 284.6 m².</p>
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<p>The area is approximately 284.6 m².</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>If the side length is 7 m, the formula Area = 2 × (1 + √2) × a² is used.</p>
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<p>If the side length is 7 m, the formula Area = 2 × (1 + √2) × a² is used.</p>
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<p>So, the area = 2 × (1 + √2) × 7² = 2 × 2.414 × 49 = 284.6 m².</p>
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<p>So, the area = 2 × (1 + √2) × 7² = 2 × 2.414 × 49 = 284.6 m².</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>Calculate the area of a regular octagon with a side length of 10 cm.</p>
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<p>Calculate the area of a regular octagon with a side length of 10 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>The area is approximately 482.8 cm².</p>
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<p>The area is approximately 482.8 cm².</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>To find the area, use the formula Area = 2 × (1 + √2) × a².</p>
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<p>To find the area, use the formula Area = 2 × (1 + √2) × a².</p>
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<p>Here, a is 10 cm. So, Area = 2 × (1 + √2) × 10² = 2 × 2.414 × 100 = 482.8 cm².</p>
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<p>Here, a is 10 cm. So, Area = 2 × (1 + √2) × 10² = 2 × 2.414 × 100 = 482.8 cm².</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 4</h3>
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<h3>Problem 4</h3>
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<p>Find the area of a regular octagon with a side length of 15 inches.</p>
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<p>Find the area of a regular octagon with a side length of 15 inches.</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>The area is approximately 1309.6 in².</p>
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<p>The area is approximately 1309.6 in².</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Using the side length of 15 in, the area is calculated as Area = 2 × (1 + √2) × 15² = 2 × 2.414 × 225 = 1309.6 in².</p>
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<p>Using the side length of 15 in, the area is calculated as Area = 2 × (1 + √2) × 15² = 2 × 2.414 × 225 = 1309.6 in².</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 5</h3>
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<h3>Problem 5</h3>
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<p>Help Lisa find the area of her regular octagon-shaped garden if each side is 8 m long.</p>
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<p>Help Lisa find the area of her regular octagon-shaped garden if each side is 8 m long.</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>The area is approximately 309.0 m².</p>
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<p>The area is approximately 309.0 m².</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>The side length is 8 m.</p>
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<p>The side length is 8 m.</p>
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<p>Use the formula Area = 2 × (1 + √2) × a² = 2 × 2.414 × 64 = 309.0 m².</p>
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<p>Use the formula Area = 2 × (1 + √2) × a² = 2 × 2.414 × 64 = 309.0 m².</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 Octagon</h2>
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<h2>FAQs on Area of Octagon</h2>
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<h3>1.Can the area of an octagon be negative?</h3>
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<h3>1.Can the area of an octagon be negative?</h3>
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<p>No, the area of an octagon can never be negative. The area of any shape will always be positive.</p>
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<p>No, the area of an octagon 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 octagon if the side length is given?</h3>
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<h3>2.How to find the area of an octagon if the side length is given?</h3>
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<p>If the side length is given, the area can be found using the formula Area = 2 × (1 + √2) × a².</p>
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<p>If the side length is given, the area can be found using the formula Area = 2 × (1 + √2) × a².</p>
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<h3>3.How to find the area of an irregular octagon?</h3>
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<h3>3.How to find the area of an irregular octagon?</h3>
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<p>For an irregular octagon, divide it into known shapes like triangles or rectangles and sum their areas.</p>
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<p>For an irregular octagon, divide it into known shapes like triangles or rectangles and sum their areas.</p>
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<h3>4.How is the perimeter of an octagon calculated?</h3>
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<h3>4.How is the perimeter of an octagon calculated?</h3>
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<p>The perimeter of a regular octagon is calculated using the formula P = 8 × a, where 'a' is the side length.</p>
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<p>The perimeter of a regular octagon is calculated using the formula P = 8 × a, where 'a' is the side length.</p>
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<h3>5.What is meant by the area of an octagon?</h3>
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<h3>5.What is meant by the area of an octagon?</h3>
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<p>The area of an octagon is the total space occupied by the octagon.</p>
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<p>The area of an octagon is the total space occupied by the octagon.</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>