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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 the ellipse.</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 ellipse.</p>
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<h2>What is the Area of Ellipse?</h2>
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<h2>What is the Area of Ellipse?</h2>
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<p>An ellipse is a two-dimensional shape that looks like an elongated circle. It has two axes: the major axis, which is the longest diameter, and the<a>minor</a>axis, which is the shortest diameter.</p>
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<p>An ellipse is a two-dimensional shape that looks like an elongated circle. It has two axes: the major axis, which is the longest diameter, and the<a>minor</a>axis, which is the shortest diameter.</p>
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<p>The area<a>of</a>the ellipse is the total space it encloses.</p>
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<p>The area<a>of</a>the ellipse is the total space it encloses.</p>
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<h2>Area of the Ellipse Formula</h2>
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<h2>Area of the Ellipse Formula</h2>
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<p>To find the area of the ellipse, we use the<a>formula</a>: π × a × b, where a and b are the semi-major and semi-minor axes, respectively.</p>
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<p>To find the area of the ellipse, we use the<a>formula</a>: π × a × b, where a and b are the semi-major and semi-minor axes, respectively.</p>
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<p>Derivation of the formula:- An ellipse is essentially a stretched circle, and its area can be thought of as a scaled version of a circle's area. The area of a circle is πr². For an ellipse, the radius is replaced by the semi-major and semi-minor axes. Therefore, the area of the ellipse = π × a × b</p>
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<p>Derivation of the formula:- An ellipse is essentially a stretched circle, and its area can be thought of as a scaled version of a circle's area. The area of a circle is πr². For an ellipse, the radius is replaced by the semi-major and semi-minor axes. Therefore, the area of the ellipse = π × a × b</p>
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<h2>How to Find the Area of Ellipse?</h2>
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<h2>How to Find the Area of Ellipse?</h2>
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<p>We can find the area of the ellipse using the formula where the semi-major and semi-minor axes are commonly used. The area of the ellipse is calculated as follows:</p>
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<p>We can find the area of the ellipse using the formula where the semi-major and semi-minor axes are commonly used. The area of the ellipse is calculated as follows:</p>
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<p>Method Using the Semi-Major and Semi-Minor Axes</p>
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<p>Method Using the Semi-Major and Semi-Minor Axes</p>
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<p>If the semi-major axis a and the semi-minor axis b are given, we find the area of the ellipse using the formula: Area = π × a × b</p>
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<p>If the semi-major axis a and the semi-minor axis b are given, we find the area of the ellipse using the formula: Area = π × a × b</p>
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<p>For example, if a and b are 5 cm and 3 cm, respectively, what will be the area of the ellipse? Area = π × a × b = π × 5 × 3 = 15π The area of the ellipse is 15π cm²</p>
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<p>For example, if a and b are 5 cm and 3 cm, respectively, what will be the area of the ellipse? Area = π × a × b = π × 5 × 3 = 15π The area of the ellipse is 15π cm²</p>
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<h2>Unit of Area of Ellipse</h2>
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<h2>Unit of Area of Ellipse</h2>
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<p>We measure the area of an ellipse 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 ellipse 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 Ellipse</h2>
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<h2>Special Cases or Variations for the Area of Ellipse</h2>
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<p>There are no special formulas for the area of an ellipse since it is calculated using the semi-major and semi-minor axes. However, understanding the orientation and the axes can be critical:</p>
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<p>There are no special formulas for the area of an ellipse since it is calculated using the semi-major and semi-minor axes. However, understanding the orientation and the axes can be critical:</p>
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<p><strong>Case 1:</strong>Circular Shape If the ellipse becomes a circle (a = b), the area is calculated using the formula for a circle, Area = πr², where r is the radius.</p>
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<p><strong>Case 1:</strong>Circular Shape If the ellipse becomes a circle (a = b), the area is calculated using the formula for a circle, Area = πr², where r is the radius.</p>
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<p><strong>Case 2:</strong>Rotated Ellipse If the ellipse is rotated but the axes are given, use the formula Area = π × a × b for the calculation.</p>
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<p><strong>Case 2:</strong>Rotated Ellipse If the ellipse is rotated but the axes are given, use the formula Area = π × a × b for the calculation.</p>
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<h2>Tips and Tricks for Area of Ellipse</h2>
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<h2>Tips and Tricks for Area of Ellipse</h2>
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<p>To ensure that you get correct results while calculating the area of the ellipse, here are some tips and tricks you should know about:</p>
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<p>To ensure that you get correct results while calculating the area of the ellipse, here are some tips and tricks you should know about:</p>
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<ul><li>The semi-major and semi-minor axes are distinct and should not be confused. </li>
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<ul><li>The semi-major and semi-minor axes are distinct and should not be confused. </li>
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<li>Ensure you use the correct units when calculating the area, and convert if necessary to maintain consistency. π is approximately 3.14159, but using a<a>calculator</a>with a π<a>function</a>is more precise.</li>
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<li>Ensure you use the correct units when calculating the area, and convert if necessary to maintain consistency. π is approximately 3.14159, but using a<a>calculator</a>with a π<a>function</a>is more precise.</li>
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</ul><h2>Common Mistakes and How to Avoid Them in Area of Ellipse</h2>
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</ul><h2>Common Mistakes and How to Avoid Them in Area of Ellipse</h2>
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<p>It is common for students to make mistakes while finding the area of the ellipse. 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 the ellipse. 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 semi-major axis a and semi-minor axis b of an elliptical garden are given as 7 m and 4 m. What will be the area?</p>
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<p>The semi-major axis a and semi-minor axis b of an elliptical garden are given as 7 m and 4 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 28π m²</p>
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<p>We will find the area as 28π m²</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Here, the semi-major axis a is 7 m and the semi-minor axis b is 4 m.</p>
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<p>Here, the semi-major axis a is 7 m and the semi-minor axis b is 4 m.</p>
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<p>The area of the ellipse = π × a × b = π × 7 × 4 = 28π m²</p>
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<p>The area of the ellipse = π × a × b = π × 7 × 4 = 28π 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 ellipse if the semi-major axis is 8 cm and the semi-minor axis is 5 cm?</p>
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<p>What will be the area of the ellipse if the semi-major axis is 8 cm and the semi-minor axis 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 40π cm²</p>
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<p>We will find the area as 40π cm²</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>If the semi-major and semi-minor axes are given, we use the formula, area of the ellipse = π × a × b.</p>
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<p>If the semi-major and semi-minor axes are given, we use the formula, area of the ellipse = π × a × b.</p>
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<p>Here, a and b are 8 cm and 5 cm.</p>
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<p>Here, a and b are 8 cm and 5 cm.</p>
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<p>Hence, the area will be π × 8 × 5 = 40π cm²</p>
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<p>Hence, the area will be π × 8 × 5 = 40π 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 the ellipse is 36π m² and the length of the semi-major axis a is 6 m.</p>
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<p>The area of the ellipse is 36π m² and the length of the semi-major axis a is 6 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>We find the length of the semi-minor axis b as 6 m</p>
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<p>We find the length of the semi-minor axis b as 6 m</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>To find the semi-minor axis, use the formula area = π × a × b.</p>
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<p>To find the semi-minor axis, use the formula area = π × a × b.</p>
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<p>Here, the area of the ellipse is given as 36π m², and the length of semi-major axis a is 6 m.</p>
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<p>Here, the area of the ellipse is given as 36π m², and the length of semi-major axis a is 6 m.</p>
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<p>Substitute the values: 36π = π × 6 × b 36 = 6 × b b = 36/6 = 6</p>
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<p>Substitute the values: 36π = π × 6 × b 36 = 6 × b b = 36/6 = 6</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 the ellipse if its semi-major axis is 10 cm and the semi-minor axis is 7 cm.</p>
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<p>Find the area of the ellipse if its semi-major axis is 10 cm and the semi-minor axis is 7 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 70π cm²</p>
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<p>We will find the area as 70π cm²</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>The given semi-major axis is 10 cm and the semi-minor axis is 7 cm.</p>
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<p>The given semi-major axis is 10 cm and the semi-minor axis is 7 cm.</p>
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<p>If the axes are given, we find the area of the ellipse using the formula π × a × b.</p>
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<p>If the axes are given, we find the area of the ellipse using the formula π × a × b.</p>
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<p>Substituting the values in the formula: Area = π × 10 × 7 = 70π cm²</p>
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<p>Substituting the values in the formula: Area = π × 10 × 7 = 70π cm²</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 Linda find the area of the ellipse if the semi-major axis is 9 m and the semi-minor axis is 3 m.</p>
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<p>Help Linda find the area of the ellipse if the semi-major axis is 9 m and the semi-minor axis is 3 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>We will find the area as 27π m²</p>
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<p>We will find the area as 27π m²</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>The semi-major axis is 9 m and the semi-minor axis is 3 m.</p>
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<p>The semi-major axis is 9 m and the semi-minor axis is 3 m.</p>
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<p>We calculate the area using the formula π × a × b.</p>
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<p>We calculate the area using the formula π × a × b.</p>
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<p>Hence, we find the area of the ellipse as π × 9 × 3 = 27π m²</p>
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<p>Hence, we find the area of the ellipse as π × 9 × 3 = 27π 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 Ellipse</h2>
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<h2>FAQs on Area of Ellipse</h2>
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<h3>1.Is it possible for the area of the ellipse to be negative?</h3>
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<h3>1.Is it possible for the area of the ellipse to be negative?</h3>
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<p>No, the area of the ellipse can never be negative. The area of any shape will always be positive.</p>
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<p>No, the area of the ellipse 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 ellipse if the lengths of the axes are given?</h3>
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<h3>2.How to find the area of an ellipse if the lengths of the axes are given?</h3>
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<p>If the semi-major and semi-minor axes are given, then we find the area using the formula, area = π × a × b</p>
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<p>If the semi-major and semi-minor axes are given, then we find the area using the formula, area = π × a × b</p>
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<h3>3.How to find the area of an ellipse if only the diameter is given?</h3>
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<h3>3.How to find the area of an ellipse if only the diameter is given?</h3>
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<p>If only the diameter is given, divide it by 2 to find the semi-major or semi-minor axis, and then use the formula area = π × a × b.</p>
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<p>If only the diameter is given, divide it by 2 to find the semi-major or semi-minor axis, and then use the formula area = π × a × b.</p>
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<h3>4.How is the circumference of the ellipse calculated?</h3>
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<h3>4.How is the circumference of the ellipse calculated?</h3>
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<p>The circumference of an ellipse does not have a simple formula like a circle. However, an approximate formula is C ≈ π × [3(a+b) - sqrt((3a+b)(a+3b))].</p>
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<p>The circumference of an ellipse does not have a simple formula like a circle. However, an approximate formula is C ≈ π × [3(a+b) - sqrt((3a+b)(a+3b))].</p>
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<h3>5.What is meant by the area of the ellipse?</h3>
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<h3>5.What is meant by the area of the ellipse?</h3>
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<p>The area of the ellipse is the total space occupied by the ellipse.</p>
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<p>The area of the ellipse is the total space occupied by the ellipse.</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>