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2026-01-01
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<p>Last updated on<strong>September 15, 2025</strong></p>
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<p>Last updated on<strong>September 15, 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 a polygon.</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 a polygon.</p>
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<h2>What is the Area of a Polygon?</h2>
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<h2>What is the Area of a Polygon?</h2>
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<p>A polygon is a two-dimensional figure with three or more straight sides. The area<a>of</a>a polygon is the total space it encloses.</p>
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<p>A polygon is a two-dimensional figure with three or more straight sides. The area<a>of</a>a polygon is the total space it encloses.</p>
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<p>The most common types of polygons include triangles, rectangles, and pentagons, each with specific<a>formulas</a>to calculate their area based on their dimensions and properties.</p>
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<p>The most common types of polygons include triangles, rectangles, and pentagons, each with specific<a>formulas</a>to calculate their area based on their dimensions and properties.</p>
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<h2>Area of a Polygon Formula</h2>
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<h2>Area of a Polygon Formula</h2>
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<p>The formula for finding the area of a polygon depends on the type of polygon. For example, the area A of a regular polygon can be calculated using the formula: A = (1/2) × Perimeter × Apothem, where the apothem is the distance from the center to the midpoint of a side.</p>
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<p>The formula for finding the area of a polygon depends on the type of polygon. For example, the area A of a regular polygon can be calculated using the formula: A = (1/2) × Perimeter × Apothem, where the apothem is the distance from the center to the midpoint of a side.</p>
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<p>For irregular polygons, the area can be determined by dividing the polygon into simpler shapes, such as triangles, and summing their areas.</p>
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<p>For irregular polygons, the area can be determined by dividing the polygon into simpler shapes, such as triangles, and summing their areas.</p>
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<h2>How to Find the Area of a Polygon?</h2>
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<h2>How to Find the Area of a Polygon?</h2>
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<p>We can find the area of a polygon using various methods depending on the information available. They are: Method for Regular Polygons For regular polygons, use the formula A = (1/2) × Perimeter × Apothem.</p>
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<p>We can find the area of a polygon using various methods depending on the information available. They are: Method for Regular Polygons For regular polygons, use the formula A = (1/2) × Perimeter × Apothem.</p>
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<p>Method for Irregular Polygons Divide the polygon into triangles and calculate the area of each triangle, then<a>sum</a>them up.</p>
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<p>Method for Irregular Polygons Divide the polygon into triangles and calculate the area of each triangle, then<a>sum</a>them up.</p>
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<p>Method Using Coordinates For a polygon with vertices given as coordinates, use the Shoelace formula: A = (1/2) × |Σ(x_i*y_(<a>i</a>+1) - y_i*x_(i+1))|, where the sum is over all the vertices and the last vertex is connected back to the first.</p>
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<p>Method Using Coordinates For a polygon with vertices given as coordinates, use the Shoelace formula: A = (1/2) × |Σ(x_i*y_(<a>i</a>+1) - y_i*x_(i+1))|, where the sum is over all the vertices and the last vertex is connected back to the first.</p>
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<h2>Unit of Area of Polygon</h2>
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<h2>Unit of Area of Polygon</h2>
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<p>We measure the area of a polygon in<a>square</a>units.</p>
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<p>We measure the area of a polygon in<a>square</a>units.</p>
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<p>The<a>measurement</a>depends on the system used:</p>
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<p>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 Polygons</h2>
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<h2>Special Cases or Variations for the Area of Polygons</h2>
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<p>Depending on the type of polygon and the given dimensions, different methods are used to calculate the area. Here are some special cases:</p>
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<p>Depending on the type of polygon and the given dimensions, different methods are used to calculate the area. Here are some special cases:</p>
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<p><strong>Case 1:</strong>Regular Polygons If the polygon is regular (all sides and angles are equal), use the formula A = (1/2) × Perimeter × Apothem.</p>
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<p><strong>Case 1:</strong>Regular Polygons If the polygon is regular (all sides and angles are equal), use the formula A = (1/2) × Perimeter × Apothem.</p>
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<p><strong>Case 2:</strong>Triangular Decomposition For irregular polygons, divide the shape into triangles and sum their areas.</p>
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<p><strong>Case 2:</strong>Triangular Decomposition For irregular polygons, divide the shape into triangles and sum their areas.</p>
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<p><strong>Case 3:</strong>Coordinate Method For polygons with vertices given as coordinates, apply the Shoelace formula for a straightforward calculation.</p>
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<p><strong>Case 3:</strong>Coordinate Method For polygons with vertices given as coordinates, apply the Shoelace formula for a straightforward calculation.</p>
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<h2>Tips and Tricks for Area of Polygons</h2>
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<h2>Tips and Tricks for Area of Polygons</h2>
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<p>To ensure accurate results when calculating the area of polygons, consider the following tips and tricks:</p>
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<p>To ensure accurate results when calculating the area of polygons, consider the following tips and tricks:</p>
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<ul><li>Always verify the type of polygon to select the appropriate formula. </li>
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<ul><li>Always verify the type of polygon to select the appropriate formula. </li>
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<li>For regular polygons, ensure accurate measurement of the apothem. </li>
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<li>For regular polygons, ensure accurate measurement of the apothem. </li>
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<li>Use the Shoelace formula for polygons with coordinate<a>data</a>to avoid manual errors.</li>
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<li>Use the Shoelace formula for polygons with coordinate<a>data</a>to avoid manual errors.</li>
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</ul><h2>Common Mistakes and How to Avoid Them in Area of Polygons</h2>
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</ul><h2>Common Mistakes and How to Avoid Them in Area of Polygons</h2>
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<p>It is common for students to make mistakes while finding the area of polygons. Let’s take a look at some mistakes made by students.</p>
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<p>It is common for students to make mistakes while finding the area of polygons. Let’s take a look at some mistakes made by students.</p>
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<h3>Problem 1</h3>
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<h3>Problem 1</h3>
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<p>The perimeter of a regular hexagon is 60 cm, and its apothem is 5 cm. What will be the area?</p>
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<p>The perimeter of a regular hexagon is 60 cm, and its apothem is 5 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>We will find the area as 150 cm²</p>
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<p>We will find the area as 150 cm²</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>For a regular hexagon, use the formula:</p>
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<p>For a regular hexagon, use the formula:</p>
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<p>A = (1/2) × Perimeter × Apothem.</p>
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<p>A = (1/2) × Perimeter × Apothem.</p>
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<p>A = (1/2) × 60 × 5 = 150 cm²</p>
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<p>A = (1/2) × 60 × 5 = 150 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>Find the area of a polygon with vertices at (1,1), (4,1), (4,5), and (1,5).</p>
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<p>Find the area of a polygon with vertices at (1,1), (4,1), (4,5), and (1,5).</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 12 square units.</p>
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<p>The area is 12 square units.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Using the Shoelace formula for the vertices (1,1), (4,1), (4,5), (1,5), we compute:</p>
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<p>Using the Shoelace formula for the vertices (1,1), (4,1), (4,5), (1,5), we compute:</p>
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<p>A = (1/2) × |(1*1 + 4*5 + 4*5 + 1*1) - (1*4 + 1*4 + 5*1 + 5*1)| = 12 square units.</p>
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<p>A = (1/2) × |(1*1 + 4*5 + 4*5 + 1*1) - (1*4 + 1*4 + 5*1 + 5*1)| = 12 square units.</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>A regular pentagon has a side length of 8 m and an apothem of 5.5 m. What is the area?</p>
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<p>A regular pentagon has a side length of 8 m and an apothem of 5.5 m. What is 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 find the area as 110 m²</p>
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<p>We find the area as 110 m²</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>For a regular pentagon, use the formula:</p>
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<p>For a regular pentagon, use the formula:</p>
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<p>A = (1/2) × Perimeter × Apothem.</p>
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<p>A = (1/2) × Perimeter × Apothem.</p>
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<p>Perimeter = 5 × 8 = 40 m.</p>
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<p>Perimeter = 5 × 8 = 40 m.</p>
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<p>A = (1/2) × 40 × 5.5 = 110 m²</p>
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<p>A = (1/2) × 40 × 5.5 = 110 m²</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>Calculate the area of a triangle with vertices at (2,3), (6,7), and (8,3).</p>
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<p>Calculate the area of a triangle with vertices at (2,3), (6,7), and (8,3).</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 12 square units.</p>
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<p>The area is 12 square units.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Using the Shoelace formula for vertices (2,3), (6,7), and (8,3), we have:</p>
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<p>Using the Shoelace formula for vertices (2,3), (6,7), and (8,3), we have:</p>
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<p>A = (1/2) × |(2*7 + 6*3 + 8*3) - (3*6 + 7*8 + 3*2)| = 12 square units.</p>
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<p>A = (1/2) × |(2*7 + 6*3 + 8*3) - (3*6 + 7*8 + 3*2)| = 12 square units.</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 Sarah find the area of a regular octagon with a side length of 10 cm and an apothem of 12 cm.</p>
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<p>Help Sarah find the area of a regular octagon with a side length of 10 cm and an apothem of 12 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 480 cm²</p>
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<p>The area is 480 cm²</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>For a regular octagon, use the formula:</p>
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<p>For a regular octagon, use the formula:</p>
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<p>A = (1/2) × Perimeter × Apothem.</p>
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<p>A = (1/2) × Perimeter × Apothem.</p>
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<p>Perimeter = 8 × 10 = 80 cm.</p>
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<p>Perimeter = 8 × 10 = 80 cm.</p>
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<p>A = (1/2) × 80 × 12 = 480 cm²</p>
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<p>A = (1/2) × 80 × 12 = 480 cm²</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 Polygons</h2>
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<h2>FAQs on Area of Polygons</h2>
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<h3>1.Can the area of a polygon be negative?</h3>
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<h3>1.Can the area of a polygon be negative?</h3>
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<p>No, the area of a polygon can never be negative. The area of any shape will always be positive.</p>
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<p>No, the area of a polygon 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 a regular polygon if the side length and apothem are given?</h3>
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<h3>2.How to find the area of a regular polygon if the side length and apothem are given?</h3>
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<p>If the side length and apothem of a regular polygon are given, use the formula A = (1/2) × Perimeter × Apothem.</p>
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<p>If the side length and apothem of a regular polygon are given, use the formula A = (1/2) × Perimeter × Apothem.</p>
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<h3>3.How to find the area of an irregular polygon using coordinates?</h3>
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<h3>3.How to find the area of an irregular polygon using coordinates?</h3>
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<p>For an irregular polygon with coordinates, use the Shoelace formula: A = (1/2) × |Σ(x_i*y_(i+1) - y_i*x_(i+1))|.</p>
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<p>For an irregular polygon with coordinates, use the Shoelace formula: A = (1/2) × |Σ(x_i*y_(i+1) - y_i*x_(i+1))|.</p>
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<h3>4.How is the perimeter of a regular polygon calculated?</h3>
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<h3>4.How is the perimeter of a regular polygon calculated?</h3>
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<p>The perimeter of a regular polygon is calculated by multiplying the<a>number</a>of sides by the length of one side.</p>
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<p>The perimeter of a regular polygon is calculated by multiplying the<a>number</a>of sides by the length of one side.</p>
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<h3>5.What is meant by the area of a polygon?</h3>
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<h3>5.What is meant by the area of a polygon?</h3>
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<p>The area of a polygon is the total space enclosed within its sides.</p>
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<p>The area of a polygon is the total space enclosed within its sides.</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>