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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 pyramid.</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 pyramid.</p>
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<h2>What is the Area of Pyramid?</h2>
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<h2>What is the Area of Pyramid?</h2>
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<p>A pyramid is a three-dimensional shape with a polygonal<a>base</a>and triangular faces that converge at a single point called the apex.</p>
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<p>A pyramid is a three-dimensional shape with a polygonal<a>base</a>and triangular faces that converge at a single point called the apex.</p>
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<p>The area<a>of</a>a pyramid includes its base area and the lateral surface area, which is the<a>sum</a>of the areas of its triangular faces.</p>
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<p>The area<a>of</a>a pyramid includes its base area and the lateral surface area, which is the<a>sum</a>of the areas of its triangular faces.</p>
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<h2>Area of the Pyramid Formula</h2>
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<h2>Area of the Pyramid Formula</h2>
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<p>To find the total surface area of a pyramid, we calculate the base area and the lateral surface area. The total surface area is given by:</p>
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<p>To find the total surface area of a pyramid, we calculate the base area and the lateral surface area. The total surface area is given by:</p>
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<p>Total Surface Area = Base Area + Lateral Surface Area. Let's see how these components are determined.</p>
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<p>Total Surface Area = Base Area + Lateral Surface Area. Let's see how these components are determined.</p>
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<p>Base Area: The base area depends on the shape of the base. For example, if the base is a<a>square</a>with side length 's', then the base area is s².</p>
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<p>Base Area: The base area depends on the shape of the base. For example, if the base is a<a>square</a>with side length 's', then the base area is s².</p>
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<p>Lateral Surface Area: The lateral surface area is the sum of the areas of the triangular faces. For a pyramid with a square base, the lateral surface area is 1/2 × perimeter of base × slant height. Therefore, Total Surface Area = Base Area + 1/2 × Perimeter of Base × Slant Height</p>
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<p>Lateral Surface Area: The lateral surface area is the sum of the areas of the triangular faces. For a pyramid with a square base, the lateral surface area is 1/2 × perimeter of base × slant height. Therefore, Total Surface Area = Base Area + 1/2 × Perimeter of Base × Slant Height</p>
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<h2>How to Find the Area of Pyramid?</h2>
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<h2>How to Find the Area of Pyramid?</h2>
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<p>We can find the area of the pyramid using specific methods, based on its base shape. The area of the pyramid is found using these steps:</p>
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<p>We can find the area of the pyramid using specific methods, based on its base shape. The area of the pyramid is found using these steps:</p>
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<p>1. Determine the base area based on its shape.</p>
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<p>1. Determine the base area based on its shape.</p>
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<p>2. Calculate the lateral surface area using the slant height and base perimeter.</p>
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<p>2. Calculate the lateral surface area using the slant height and base perimeter.</p>
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<p>3. Add the base area to the lateral surface area for the total surface area.</p>
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<p>3. Add the base area to the lateral surface area for the total surface area.</p>
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<p>Example for a Pyramid with a Square Base: If the side of the square base is 6 cm and the slant height is 10 cm, the base area is 6 × 6 = 36 cm².</p>
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<p>Example for a Pyramid with a Square Base: If the side of the square base is 6 cm and the slant height is 10 cm, the base area is 6 × 6 = 36 cm².</p>
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<p>The perimeter of the base is 4 × 6 = 24 cm. The lateral surface area is 1/2 × 24 × 10 = 120 cm². Therefore, the total surface area is 36 + 120 = 156 cm².</p>
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<p>The perimeter of the base is 4 × 6 = 24 cm. The lateral surface area is 1/2 × 24 × 10 = 120 cm². Therefore, the total surface area is 36 + 120 = 156 cm².</p>
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<h2>Unit of Area of Pyramid</h2>
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<h2>Unit of Area of Pyramid</h2>
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<p>We measure the area of a pyramid in square units. The<a>measurement</a>depends on the system used:</p>
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<p>We measure the area of a pyramid in square 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 Pyramid</h2>
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<h2>Special Cases or Variations for the Area of Pyramid</h2>
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<p>The method for calculating the area of a pyramid can change based on the shape of its base. Here are some special cases:</p>
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<p>The method for calculating the area of a pyramid can change based on the shape of its base. Here are some special cases:</p>
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<p><strong>Case 1:</strong>Pyramid with a Square Base For a square base, calculate the base area as s² and the lateral surface area as 1/2 × perimeter of base × slant height.</p>
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<p><strong>Case 1:</strong>Pyramid with a Square Base For a square base, calculate the base area as s² and the lateral surface area as 1/2 × perimeter of base × slant height.</p>
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<p><strong>Case 2:</strong>Pyramid with a Rectangular Base For a rectangular base, the base area is length × width, and the lateral surface area is calculated using the slant heights of the triangular faces.</p>
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<p><strong>Case 2:</strong>Pyramid with a Rectangular Base For a rectangular base, the base area is length × width, and the lateral surface area is calculated using the slant heights of the triangular faces.</p>
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<p><strong>Case 3:</strong>Pyramid with a Triangular Base Use the<a>formula</a>for the area of a triangle for the base area and add the lateral areas of the other triangles.</p>
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<p><strong>Case 3:</strong>Pyramid with a Triangular Base Use the<a>formula</a>for the area of a triangle for the base area and add the lateral areas of the other triangles.</p>
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<h2>Tips and Tricks for Area of Pyramid</h2>
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<h2>Tips and Tricks for Area of Pyramid</h2>
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<p>To ensure<a>accuracy</a>when calculating the area of a pyramid, consider these tips and tricks: </p>
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<p>To ensure<a>accuracy</a>when calculating the area of a pyramid, consider these tips and tricks: </p>
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<ul><li>Ensure correct measurement of the slant height, as it differs from the height of the pyramid. </li>
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<ul><li>Ensure correct measurement of the slant height, as it differs from the height of the pyramid. </li>
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<li>The base area calculation depends on the shape of the base. Use the appropriate formula for the base. </li>
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<li>The base area calculation depends on the shape of the base. Use the appropriate formula for the base. </li>
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<li>Confirm the correct units are used for all measurements to maintain consistency.</li>
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<li>Confirm the correct units are used for all measurements to maintain consistency.</li>
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</ul><h2>Common Mistakes and How to Avoid Them in Area of Pyramid</h2>
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</ul><h2>Common Mistakes and How to Avoid Them in Area of Pyramid</h2>
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<p>It is common for students to make mistakes while finding the area of a pyramid. 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 a pyramid. 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>A pyramid has a square base with a side length of 8 m and a slant height of 12 m. What is the total surface area?</p>
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<p>A pyramid has a square base with a side length of 8 m and a slant height of 12 m. What is the total surface 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 total surface area as 272 m².</p>
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<p>We will find the total surface area as 272 m².</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>The base area is 8 × 8 = 64 m².</p>
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<p>The base area is 8 × 8 = 64 m².</p>
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<p>The perimeter of the base is 4 × 8 = 32 m.</p>
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<p>The perimeter of the base is 4 × 8 = 32 m.</p>
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<p>The lateral surface area is 1/2 × 32 × 12 = 192 m².</p>
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<p>The lateral surface area is 1/2 × 32 × 12 = 192 m².</p>
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<p>The total surface area is 64 + 192 = 272 m².</p>
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<p>The total surface area is 64 + 192 = 272 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 a pyramid with a rectangular base measuring 5 cm by 10 cm and a slant height of 7 cm?</p>
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<p>What will be the area of a pyramid with a rectangular base measuring 5 cm by 10 cm and a slant height of 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 total surface area as 135 cm².</p>
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<p>We will find the total surface area as 135 cm².</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>The base area is 5 × 10 = 50 cm².</p>
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<p>The base area is 5 × 10 = 50 cm².</p>
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<p>The perimeter of the base is 2(5 + 10) = 30 cm.</p>
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<p>The perimeter of the base is 2(5 + 10) = 30 cm.</p>
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<p>The lateral surface area is 1/2 × 30 × 7 = 105 cm².</p>
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<p>The lateral surface area is 1/2 × 30 × 7 = 105 cm².</p>
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<p>The total surface area is 50 + 105 = 155 cm².</p>
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<p>The total surface area is 50 + 105 = 155 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>A triangular pyramid has a base with sides of 6 m each and a slant height of 8 m. What is the total surface area?</p>
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<p>A triangular pyramid has a base with sides of 6 m each and a slant height of 8 m. What is the total surface 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 total surface area as 103.92 m².</p>
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<p>We find the total surface area as 103.92 m².</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>The base area is (sqrt(3)/4)s² = (sqrt(3)/4)(6)² = 15.59 m².</p>
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<p>The base area is (sqrt(3)/4)s² = (sqrt(3)/4)(6)² = 15.59 m².</p>
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<p>The perimeter of the base is 3 × 6 = 18 m.</p>
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<p>The perimeter of the base is 3 × 6 = 18 m.</p>
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<p>The lateral surface area is 1/2 × 18 × 8 = 72 m².</p>
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<p>The lateral surface area is 1/2 × 18 × 8 = 72 m².</p>
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<p>The total surface area is 15.59 + 72 = 87.59 m².</p>
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<p>The total surface area is 15.59 + 72 = 87.59 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>Find the area of a pyramid with a hexagonal base where each side of the base is 4 cm and the slant height is 9 cm.</p>
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<p>Find the area of a pyramid with a hexagonal base where each side of the base is 4 cm and the slant height is 9 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 total surface area as 155.88 cm².</p>
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<p>We will find the total surface area as 155.88 cm².</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>The base area is (3√3/2)s² = (3√3/2)(4)² = 41.57 cm².</p>
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<p>The base area is (3√3/2)s² = (3√3/2)(4)² = 41.57 cm².</p>
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<p>The perimeter of the base is 6 × 4 = 24 cm.</p>
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<p>The perimeter of the base is 6 × 4 = 24 cm.</p>
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<p>The lateral surface area is 1/2 × 24 × 9 = 108 cm².</p>
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<p>The lateral surface area is 1/2 × 24 × 9 = 108 cm².</p>
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<p>The total surface area is 41.57 + 108 = 149.57 cm².</p>
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<p>The total surface area is 41.57 + 108 = 149.57 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 Sarah find the area of a pyramid with a pentagonal base, side length of 3 m, and slant height of 5 m.</p>
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<p>Help Sarah find the area of a pyramid with a pentagonal base, side length of 3 m, and slant height of 5 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 total surface area as 82.53 m².</p>
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<p>We will find the total surface area as 82.53 m².</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>The base area is (5/4)√(5(5+2√5)) × s² = 15.48 m².</p>
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<p>The base area is (5/4)√(5(5+2√5)) × s² = 15.48 m².</p>
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<p>The perimeter of the base is 5 × 3 = 15 m.</p>
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<p>The perimeter of the base is 5 × 3 = 15 m.</p>
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<p>The lateral surface area is 1/2 × 15 × 5 = 37.5 m².</p>
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<p>The lateral surface area is 1/2 × 15 × 5 = 37.5 m².</p>
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<p>The total surface area is 15.48 + 37.5 = 52.98 m².</p>
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<p>The total surface area is 15.48 + 37.5 = 52.98 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 Pyramid</h2>
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<h2>FAQs on Area of Pyramid</h2>
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<h3>1.Is it possible for the area of a pyramid to be negative?</h3>
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<h3>1.Is it possible for the area of a pyramid to be negative?</h3>
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<p>No, the area of a pyramid can never be negative. The area of any shape will always be positive.</p>
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<p>No, the area of a pyramid 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 pyramid if the slant height and base dimensions are given?</h3>
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<h3>2.How to find the area of a pyramid if the slant height and base dimensions are given?</h3>
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<p>If the slant height and base dimensions are given, calculate the base area using the base shape's formula and the lateral surface area using the slant height.</p>
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<p>If the slant height and base dimensions are given, calculate the base area using the base shape's formula and the lateral surface area using the slant height.</p>
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<h3>3.How to find the area of a pyramid if only base perimeter is given?</h3>
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<h3>3.How to find the area of a pyramid if only base perimeter is given?</h3>
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<p>You also need the slant height to calculate the lateral surface area along with the base area to find the total surface area.</p>
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<p>You also need the slant height to calculate the lateral surface area along with the base area to find the total surface area.</p>
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<h3>4.How is the volume of a pyramid calculated?</h3>
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<h3>4.How is the volume of a pyramid calculated?</h3>
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<p>The volume of a pyramid is calculated using the formula V = (1/3) × Base Area × Height, where the height is the perpendicular distance from the base to the apex.</p>
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<p>The volume of a pyramid is calculated using the formula V = (1/3) × Base Area × Height, where the height is the perpendicular distance from the base to the apex.</p>
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<h3>5.What is meant by the area of the pyramid?</h3>
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<h3>5.What is meant by the area of the pyramid?</h3>
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<p>The area of the pyramid is the total surface area, which includes the base area and the lateral surface area.</p>
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<p>The area of the pyramid is the total surface area, which includes the base area and the lateral surface area.</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>