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2026-01-01
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<p>Last updated on<strong>September 4, 2025</strong></p>
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<p>Last updated on<strong>September 4, 2025</strong></p>
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<p>A right rectangular prism is a 3-dimensional shape with six rectangular faces, where all angles are right angles. The surface area of a right rectangular prism is the total area covered by its outer surface. It includes the areas of all six faces. In this article, we will learn about the surface area of a right rectangular prism.</p>
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<p>A right rectangular prism is a 3-dimensional shape with six rectangular faces, where all angles are right angles. The surface area of a right rectangular prism is the total area covered by its outer surface. It includes the areas of all six faces. In this article, we will learn about the surface area of a right rectangular prism.</p>
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<h2>What is the Surface Area of a Right Rectangular Prism?</h2>
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<h2>What is the Surface Area of a Right Rectangular Prism?</h2>
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<p>The surface area of a right rectangular prism is the total area occupied by the faces of the prism. It is measured in<a>square</a>units.</p>
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<p>The surface area of a right rectangular prism is the total area occupied by the faces of the prism. It is measured in<a>square</a>units.</p>
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<p>A right rectangular prism, also known as a cuboid, has two rectangular bases and four lateral rectangular faces. Its six faces are composed of three pairs of opposite rectangles.</p>
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<p>A right rectangular prism, also known as a cuboid, has two rectangular bases and four lateral rectangular faces. Its six faces are composed of three pairs of opposite rectangles.</p>
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<p>The surface area is calculated by finding the area of each face and summing them all together.</p>
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<p>The surface area is calculated by finding the area of each face and summing them all together.</p>
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<h2>Surface Area of a Right Rectangular Prism Formula</h2>
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<h2>Surface Area of a Right Rectangular Prism Formula</h2>
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<p>A right rectangular prism consists of six rectangular faces: two length by width, two width by height, and two height by length.</p>
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<p>A right rectangular prism consists of six rectangular faces: two length by width, two width by height, and two height by length.</p>
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<p>The total surface area is the<a>sum</a>of the areas of these faces. The<a>formula</a>for the total surface area (TSA) of a right rectangular prism is: Total Surface Area = 2lw + 2lh + 2wh </p>
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<p>The total surface area is the<a>sum</a>of the areas of these faces. The<a>formula</a>for the total surface area (TSA) of a right rectangular prism is: Total Surface Area = 2lw + 2lh + 2wh </p>
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<p>Where l is the length, w is the width, and h is the height of the prism.</p>
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<p>Where l is the length, w is the width, and h is the height of the prism.</p>
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<h2>Understanding the Surface Area Formula</h2>
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<h2>Understanding the Surface Area Formula</h2>
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<p>The total surface area of a right rectangular prism accounts for all the faces of the prism. Each pair of opposite faces has the same area, which simplifies the calculation.</p>
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<p>The total surface area of a right rectangular prism accounts for all the faces of the prism. Each pair of opposite faces has the same area, which simplifies the calculation.</p>
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<p>The formula is derived by adding up the areas of these pairs: TSA = 2(lw + lh + wh) This formula ensures that all six faces are included in the calculation.</p>
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<p>The formula is derived by adding up the areas of these pairs: TSA = 2(lw + lh + wh) This formula ensures that all six faces are included in the calculation.</p>
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<h2>Example Problem: Surface Area Calculation</h2>
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<h2>Example Problem: Surface Area Calculation</h2>
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<p>To calculate the surface area of a right rectangular prism, measure the length, width, and height, then substitute these values into the formula.</p>
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<p>To calculate the surface area of a right rectangular prism, measure the length, width, and height, then substitute these values into the formula.</p>
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<p>For instance, if a prism has a length of 4 cm, a width of 3 cm, and a height of 5 cm, its surface area would be: TSA = 2(4 x 3 + 3 x 5 + 5 x 4) = 2(12 + 15 + 20) = 2(47) = 94 cm2 </p>
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<p>For instance, if a prism has a length of 4 cm, a width of 3 cm, and a height of 5 cm, its surface area would be: TSA = 2(4 x 3 + 3 x 5 + 5 x 4) = 2(12 + 15 + 20) = 2(47) = 94 cm2 </p>
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<h2>Volume of a Right Rectangular Prism</h2>
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<h2>Volume of a Right Rectangular Prism</h2>
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<p>The volume of a right rectangular prism shows how much space is inside it. It is calculated by multiplying the length, width, and height of the prism:</p>
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<p>The volume of a right rectangular prism shows how much space is inside it. It is calculated by multiplying the length, width, and height of the prism:</p>
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<p>Volume = l x w x h This formula tells us the capacity of the prism or how much it can hold.</p>
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<p>Volume = l x w x h This formula tells us the capacity of the prism or how much it can hold.</p>
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<h2>Ignoring the Pairing of Opposite Faces</h2>
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<h2>Ignoring the Pairing of Opposite Faces</h2>
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<p>Students may forget that opposite faces are equal in area. This can lead to errors in calculating the total surface area. Always remember that each pair of opposite faces contributes twice their area.</p>
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<p>Students may forget that opposite faces are equal in area. This can lead to errors in calculating the total surface area. Always remember that each pair of opposite faces contributes twice their area.</p>
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<h3>Problem 1</h3>
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<h3>Problem 1</h3>
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<p>Given l = 8 cm, w = 5 cm, h = 7 cm. Use the formula: \(\text{TSA} = 2(lw + lh + wh) = 2(8 \times 5 + 5 \times 7 + 7 \times 8) = 2(40 + 35 + 56) = 2(131) = 262 \text{ cm}^2\)</p>
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<p>Given l = 8 cm, w = 5 cm, h = 7 cm. Use the formula: \(\text{TSA} = 2(lw + lh + wh) = 2(8 \times 5 + 5 \times 7 + 7 \times 8) = 2(40 + 35 + 56) = 2(131) = 262 \text{ cm}^2\)</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>Find the total surface area of a right rectangular prism with length 10 cm, width 4 cm, and height 6 cm.</p>
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<p>Find the total surface area of a right rectangular prism with length 10 cm, width 4 cm, and height 6 cm.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Surface Area = 248 cm²</p>
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<p>Surface Area = 248 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>Use the formula: \(\text{TSA} = 2(lw + lh + wh) = 2(10 \times 4 + 4 \times 6 + 6 \times 10) = 2(40 + 24 + 60) = 2(124) = 248 \text{ cm}^2\)</p>
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<p>Use the formula: \(\text{TSA} = 2(lw + lh + wh) = 2(10 \times 4 + 4 \times 6 + 6 \times 10) = 2(40 + 24 + 60) = 2(124) = 248 \text{ cm}^2\)</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>A right rectangular prism has a length of 12 cm, a width of 7 cm, and a height of 9 cm. Find the surface area.</p>
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<p>A right rectangular prism has a length of 12 cm, a width of 7 cm, and a height of 9 cm. Find the surface area.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Surface Area = 678 cm²</p>
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<p>Surface Area = 678 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>Use the formula: \(\text{TSA} = 2(lw + lh + wh) = 2(12 \times 7 + 7 \times 9 + 9 \times 12) = 2(84 + 63 + 108) = 2(255) = 678 \text{ cm}^2\)</p>
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<p>Use the formula: \(\text{TSA} = 2(lw + lh + wh) = 2(12 \times 7 + 7 \times 9 + 9 \times 12) = 2(84 + 63 + 108) = 2(255) = 678 \text{ cm}^2\)</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>Calculate the surface area of a right rectangular prism with dimensions 3 cm, 4 cm, and 5 cm.</p>
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<p>Calculate the surface area of a right rectangular prism with dimensions 3 cm, 4 cm, and 5 cm.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Surface Area = 94 cm²</p>
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<p>Surface Area = 94 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>Use the formula: \(\text{TSA} = 2(lw + lh + wh) = 2(3 \times 4 + 4 \times 5 + 5 \times 3) = 2(12 + 20 + 15) = 2(47) = 94 \text{ cm}^2\)</p>
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<p>Use the formula: \(\text{TSA} = 2(lw + lh + wh) = 2(3 \times 4 + 4 \times 5 + 5 \times 3) = 2(12 + 20 + 15) = 2(47) = 94 \text{ cm}^2\)</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 surface area of a right rectangular prism is 214 cm². If its length is 7 cm and width is 5 cm, find its height.</p>
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<p>The surface area of a right rectangular prism is 214 cm². If its length is 7 cm and width is 5 cm, find its height.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Height = 6 cm</p>
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<p>Height = 6 cm</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h2>It is the total area that covers the outside of the prism, including all its rectangular faces.</h2>
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<h2>It is the total area that covers the outside of the prism, including all its rectangular faces.</h2>
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<h3>1.What is the formula for surface area of a right rectangular prism?</h3>
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<h3>1.What is the formula for surface area of a right rectangular prism?</h3>
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<p>The formula is TSA = 2lw + 2lh + 2wh where l , w , and h are the length, width, and height.</p>
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<p>The formula is TSA = 2lw + 2lh + 2wh where l , w , and h are the length, width, and height.</p>
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<h3>2.How do you differentiate surface area from volume?</h3>
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<h3>2.How do you differentiate surface area from volume?</h3>
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<p>Surface area is the total area of all outer faces of a shape, while volume measures the space inside the shape.</p>
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<p>Surface area is the total area of all outer faces of a shape, while volume measures the space inside the shape.</p>
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<h3>3.Are the opposite faces of a right rectangular prism equal?</h3>
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<h3>3.Are the opposite faces of a right rectangular prism equal?</h3>
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<p>Yes, each<a>set</a>of opposite faces in a right rectangular prism has the same area.</p>
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<p>Yes, each<a>set</a>of opposite faces in a right rectangular prism has the same area.</p>
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<h3>4.What unit is surface area measured in?</h3>
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<h3>4.What unit is surface area measured in?</h3>
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<p>Surface area is always measured in square units like cm², m², or in².</p>
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<p>Surface area is always measured in square units like cm², m², or in².</p>
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<h2>Common Mistakes and How to Avoid Them in the Surface Area of a Right Rectangular Prism</h2>
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<h2>Common Mistakes and How to Avoid Them in the Surface Area of a Right Rectangular Prism</h2>
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<p>Students often make mistakes while calculating the surface area of a right rectangular prism, leading to incorrect answers. Below are some common mistakes and ways to avoid them.</p>
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<p>Students often make mistakes while calculating the surface area of a right rectangular prism, leading to incorrect answers. Below are some common mistakes and ways to avoid them.</p>
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<p>What Is Measurement? 📏 | Easy Tricks, Units & 🎯 Fun Learning for Kids | ✨BrightCHAMPS Math</p>
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<p>What Is Measurement? 📏 | Easy Tricks, Units & 🎯 Fun Learning for Kids | ✨BrightCHAMPS Math</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>