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2026-01-01
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2026-02-28
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<p>133 Learners</p>
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<p>Last updated on<strong>September 8, 2025</strong></p>
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<p>Last updated on<strong>September 8, 2025</strong></p>
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<p>The perimeter of a shape involves the total length of its boundary. While the term "perimeter of diagonal" might not be standard, it can refer to the idea of calculating the total distance around a rectangle or square, including its diagonals. This concept is useful in various practical applications such as construction, design, and more. In this topic, we will explore the perimeter of a diagonal in the context of rectangles and squares.</p>
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<p>The perimeter of a shape involves the total length of its boundary. While the term "perimeter of diagonal" might not be standard, it can refer to the idea of calculating the total distance around a rectangle or square, including its diagonals. This concept is useful in various practical applications such as construction, design, and more. In this topic, we will explore the perimeter of a diagonal in the context of rectangles and squares.</p>
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<h2>What is the Perimeter of Diagonal?</h2>
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<h2>What is the Perimeter of Diagonal?</h2>
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<p>The<a>term</a>"perimeter of diagonal" is not typically used in standard<a>geometry</a>; however, it can be understood as the total distance around a rectangle or<a>square</a>, including its diagonals.</p>
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<p>The<a>term</a>"perimeter of diagonal" is not typically used in standard<a>geometry</a>; however, it can be understood as the total distance around a rectangle or<a>square</a>, including its diagonals.</p>
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<p>For a rectangle, if you imagine walking along all four sides and its two diagonals, you would be covering the perimeter plus the diagonals.</p>
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<p>For a rectangle, if you imagine walking along all four sides and its two diagonals, you would be covering the perimeter plus the diagonals.</p>
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<p>The<a>formula</a>for the perimeter of a rectangle is 𝑃 = 2(𝑎 + 𝑏), where a and b are the lengths of the rectangle's sides.</p>
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<p>The<a>formula</a>for the perimeter of a rectangle is 𝑃 = 2(𝑎 + 𝑏), where a and b are the lengths of the rectangle's sides.</p>
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<p>The length of the diagonal d can be found using the formula 𝑑 = √(𝑎² + 𝑏²).</p>
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<p>The length of the diagonal d can be found using the formula 𝑑 = √(𝑎² + 𝑏²).</p>
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<p>For instance, if a rectangle has sides a = 6 and b = 8, then its perimeter is p = 2(6 + 8) = 28, and the diagonal is d = √(6² + 8²) = 10.</p>
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<p>For instance, if a rectangle has sides a = 6 and b = 8, then its perimeter is p = 2(6 + 8) = 28, and the diagonal is d = √(6² + 8²) = 10.</p>
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<h2>Formula for Perimeter and Diagonal - 𝑃 = 2(𝑎 + 𝑏), 𝑑 = √(𝑎² + 𝑏²)</h2>
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<h2>Formula for Perimeter and Diagonal - 𝑃 = 2(𝑎 + 𝑏), 𝑑 = √(𝑎² + 𝑏²)</h2>
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<p>Let’s consider another example of a rectangle with side lengths 𝑎 = 8 and 𝑏 = 10.</p>
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<p>Let’s consider another example of a rectangle with side lengths 𝑎 = 8 and 𝑏 = 10.</p>
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<p>The perimeter of the rectangle will be 𝑃 = 2(𝑎 + 𝑏) = 2(8 + 10) = 36.</p>
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<p>The perimeter of the rectangle will be 𝑃 = 2(𝑎 + 𝑏) = 2(8 + 10) = 36.</p>
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<p>The diagonal length will be 𝑑 = √(8² + 10²) = √(64 + 100) = √164, approximately 12.81.</p>
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<p>The diagonal length will be 𝑑 = √(8² + 10²) = √(64 + 100) = √164, approximately 12.81.</p>
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<h2>How to Calculate the Perimeter Including Diagonals</h2>
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<h2>How to Calculate the Perimeter Including Diagonals</h2>
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<p>To find the perimeter including the diagonals of a rectangle, first calculate the perimeter of the rectangle using 𝑃 = 2(𝑎 + 𝑏). Then, add the length of the diagonal calculated using 𝑑 = √(𝑎² + 𝑏²).</p>
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<p>To find the perimeter including the diagonals of a rectangle, first calculate the perimeter of the rectangle using 𝑃 = 2(𝑎 + 𝑏). Then, add the length of the diagonal calculated using 𝑑 = √(𝑎² + 𝑏²).</p>
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<p>For example, if a rectangle has sides of a = 6, b = 6, and you wish to include the diagonals, first find the perimeter = 2(6 + 6) = 24. Then, calculate the diagonal using 𝑑 = √(6² + 6²) = √72 ≈ 8.49.</p>
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<p>For example, if a rectangle has sides of a = 6, b = 6, and you wish to include the diagonals, first find the perimeter = 2(6 + 6) = 24. Then, calculate the diagonal using 𝑑 = √(6² + 6²) = √72 ≈ 8.49.</p>
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<p>Example Problem on Perimeter including Diagonals </p>
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<p>Example Problem on Perimeter including Diagonals </p>
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<p>For finding the perimeter including the diagonal, use the formulas, 𝑃 = 2(𝑎 + 𝑏) and 𝑑 = √(𝑎² + 𝑏²). For example, let’s say, a = 5 cm, b = 4 cm.</p>
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<p>For finding the perimeter including the diagonal, use the formulas, 𝑃 = 2(𝑎 + 𝑏) and 𝑑 = √(𝑎² + 𝑏²). For example, let’s say, a = 5 cm, b = 4 cm.</p>
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<p>Now, the perimeter = 2(5 + 4) = 18 cm, and the diagonal = √(5² + 4²) = √41 ≈ 6.4 cm.</p>
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<p>Now, the perimeter = 2(5 + 4) = 18 cm, and the diagonal = √(5² + 4²) = √41 ≈ 6.4 cm.</p>
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<p>Therefore, the total distance including the diagonal is 18 + 6.4 ≈ 24.4 cm.</p>
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<p>Therefore, the total distance including the diagonal is 18 + 6.4 ≈ 24.4 cm.</p>
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<h2>Tips and Tricks for Calculating Perimeter Including Diagonals</h2>
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<h2>Tips and Tricks for Calculating Perimeter Including Diagonals</h2>
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<p>Learning some tips and tricks makes it easier for children to calculate the perimeter including diagonals. Here are some tips and tricks given below:</p>
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<p>Learning some tips and tricks makes it easier for children to calculate the perimeter including diagonals. Here are some tips and tricks given below:</p>
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<ul><li>Always remember that the perimeter of a rectangle is simply 2 times the<a>sum</a>of the lengths of its two sides. For that, use the formula, 𝑃 = 2(𝑎 + 𝑏).</li>
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<ul><li>Always remember that the perimeter of a rectangle is simply 2 times the<a>sum</a>of the lengths of its two sides. For that, use the formula, 𝑃 = 2(𝑎 + 𝑏).</li>
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</ul><ul><li>Calculating the diagonal involves using the Pythagorean theorem where the diagonal acts as the hypotenuse. The formula is: 𝑑 = √(𝑎² + 𝑏²).</li>
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</ul><ul><li>Calculating the diagonal involves using the Pythagorean theorem where the diagonal acts as the hypotenuse. The formula is: 𝑑 = √(𝑎² + 𝑏²).</li>
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</ul><ul><li>To reduce confusion, specifically arrange the indicated side lengths if you need the perimeter of a group of rectangles. After that, apply the formula to each shape.</li>
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</ul><ul><li>To reduce confusion, specifically arrange the indicated side lengths if you need the perimeter of a group of rectangles. After that, apply the formula to each shape.</li>
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</ul><ul><li>To avoid mistakes when adding the perimeter and diagonals, make sure the side lengths and diagonal lengths are precise for common uses like architecture and design. If you are given the diagonal and one side, you can use the Pythagorean theorem to find the other side.</li>
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</ul><ul><li>To avoid mistakes when adding the perimeter and diagonals, make sure the side lengths and diagonal lengths are precise for common uses like architecture and design. If you are given the diagonal and one side, you can use the Pythagorean theorem to find the other side.</li>
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</ul><h2>Common Mistakes and How to Avoid Them in Calculating Perimeter Including Diagonals</h2>
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</ul><h2>Common Mistakes and How to Avoid Them in Calculating Perimeter Including Diagonals</h2>
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<p>Did you know that while working with the perimeter including diagonals, children might encounter some errors or difficulties? We have many solutions to resolve these problems. Here are some given below:</p>
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<p>Did you know that while working with the perimeter including diagonals, children might encounter some errors or difficulties? We have many solutions to resolve these problems. Here are some given below:</p>
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<h3>Problem 1</h3>
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<h3>Problem 1</h3>
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<p>A rectangular-shaped garden has a perimeter of 48 meters and a diagonal measuring 17 meters. If the length of one side is 14 meters, what is the length of the other side?</p>
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<p>A rectangular-shaped garden has a perimeter of 48 meters and a diagonal measuring 17 meters. If the length of one side is 14 meters, what is the length of the other side?</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>Length of the other side = 10 meters.</p>
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<p>Length of the other side = 10 meters.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Let ‘b’ be the length of the other side. And the given perimeter = 48 meters. One side length = 14 meters.</p>
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<p>Let ‘b’ be the length of the other side. And the given perimeter = 48 meters. One side length = 14 meters.</p>
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<p>Perimeter of rectangle = 2(14 + b) = 48 28 + 2b = 48 2b = 48 - 28 = 20 b = 10</p>
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<p>Perimeter of rectangle = 2(14 + b) = 48 28 + 2b = 48 2b = 48 - 28 = 20 b = 10</p>
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<p>Therefore, the length of the other side is 10 meters.</p>
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<p>Therefore, the length of the other side is 10 meters.</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>A wire with a total length of 297 cm is reshaped into a square. Find the length of each side of the square and verify its diagonal.</p>
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<p>A wire with a total length of 297 cm is reshaped into a square. Find the length of each side of the square and verify its diagonal.</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>74.25 cm</p>
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<p>74.25 cm</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Given that the total length of the wire is reshaped into a square, here is the solution:</p>
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<p>Given that the total length of the wire is reshaped into a square, here is the solution:</p>
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<p>Perimeter of a square = 4 × a 297 = 4 × a 297 ÷ 4 = 74.25 a = 74.25</p>
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<p>Perimeter of a square = 4 × a 297 = 4 × a 297 ÷ 4 = 74.25 a = 74.25</p>
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<p>The diagonal of the square is 𝑑 = a√2 = 74.25√2 ≈ 105.03 cm.</p>
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<p>The diagonal of the square is 𝑑 = a√2 = 74.25√2 ≈ 105.03 cm.</p>
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<p>Therefore, each side of the square is 74.25 cm, and the diagonal is approximately 105.03 cm.</p>
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<p>Therefore, each side of the square is 74.25 cm, and the diagonal is approximately 105.03 cm.</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>Find the perimeter of a square with sides of 10 cm, and calculate the diagonal.</p>
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<p>Find the perimeter of a square with sides of 10 cm, and calculate the diagonal.</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>40 cm</p>
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<p>40 cm</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Perimeter of square = 4 × a P = 4 × 10 = 40 cm</p>
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<p>Perimeter of square = 4 × a P = 4 × 10 = 40 cm</p>
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<p>The diagonal is 𝑑 = 10√2 ≈ 14.14 cm.</p>
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<p>The diagonal is 𝑑 = 10√2 ≈ 14.14 cm.</p>
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<p>Therefore, the perimeter is 40 cm, and the diagonal length is approximately 14.14 cm.</p>
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<p>Therefore, the perimeter is 40 cm, and the diagonal length is approximately 14.14 cm.</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>Annie is designing a rectangular floor plan for her new room. The sides of the room measure: Side A = 12 meters Side B = 9 meters How long is the diagonal of the room?</p>
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<p>Annie is designing a rectangular floor plan for her new room. The sides of the room measure: Side A = 12 meters Side B = 9 meters How long is the diagonal of the room?</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 diagonal is 15 meters.</p>
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<p>The diagonal is 15 meters.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>The diagonal is calculated using the formula: 𝑑 = √(𝑎² + 𝑏²) 𝑑 = √(12² + 9²) = √(144 + 81) = √225 = 15 meters</p>
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<p>The diagonal is calculated using the formula: 𝑑 = √(𝑎² + 𝑏²) 𝑑 = √(12² + 9²) = √(144 + 81) = √225 = 15 meters</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>Calculate the perimeter including the diagonals of a rectangular book cover with sides a = 10 cm and b = 8 cm.</p>
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<p>Calculate the perimeter including the diagonals of a rectangular book cover with sides a = 10 cm and b = 8 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>Perimeter = 36 cm, Diagonal = 12.81 cm</p>
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<p>Perimeter = 36 cm, Diagonal = 12.81 cm</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>The perimeter of the rectangle is calculated as: Perimeter = 2(a + b) = 2(10 + 8) = 36 cm</p>
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<p>The perimeter of the rectangle is calculated as: Perimeter = 2(a + b) = 2(10 + 8) = 36 cm</p>
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<p>The diagonal is calculated as: Diagonal = √(10² + 8²) = √(100 + 64) = √164 ≈ 12.81 cm</p>
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<p>The diagonal is calculated as: Diagonal = √(10² + 8²) = √(100 + 64) = √164 ≈ 12.81 cm</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h2>FAQs on Perimeter Including Diagonals</h2>
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<h2>FAQs on Perimeter Including Diagonals</h2>
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<h3>1.Evaluate the perimeter of a rectangle if its sides are 3 cm and 4 cm, and calculate its diagonal.</h3>
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<h3>1.Evaluate the perimeter of a rectangle if its sides are 3 cm and 4 cm, and calculate its diagonal.</h3>
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<p>Perimeter of rectangle = 2(a + b), Hence P = 2(3 + 4) = 14 cm. Diagonal, d = √(3² + 4²) = √9 + 16 = √25 = 5 cm.</p>
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<p>Perimeter of rectangle = 2(a + b), Hence P = 2(3 + 4) = 14 cm. Diagonal, d = √(3² + 4²) = √9 + 16 = √25 = 5 cm.</p>
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<h3>2.What is meant by the perimeter including diagonals?</h3>
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<h3>2.What is meant by the perimeter including diagonals?</h3>
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<p>It refers to the total length around a rectangle or square, including the<a>measurement</a>of its diagonals.</p>
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<p>It refers to the total length around a rectangle or square, including the<a>measurement</a>of its diagonals.</p>
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<h3>3.What are the types of polygons related to diagonals?</h3>
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<h3>3.What are the types of polygons related to diagonals?</h3>
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<p>Polygons related to diagonals in this context are primarily rectangles and squares, as these shapes have diagonal lines connecting opposite corners.</p>
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<p>Polygons related to diagonals in this context are primarily rectangles and squares, as these shapes have diagonal lines connecting opposite corners.</p>
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<h3>4.Which shape has equal diagonals?</h3>
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<h3>4.Which shape has equal diagonals?</h3>
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<p>A square has equal diagonals. All sides and angles are equal, making the diagonals equal as well.</p>
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<p>A square has equal diagonals. All sides and angles are equal, making the diagonals equal as well.</p>
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<h3>5.What is the formula for finding a rectangle's diagonal?</h3>
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<h3>5.What is the formula for finding a rectangle's diagonal?</h3>
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<p>The formula for finding the diagonal of a rectangle is 𝑑 = √(𝑎² + 𝑏²), where a and b are the lengths of the rectangle's sides.</p>
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<p>The formula for finding the diagonal of a rectangle is 𝑑 = √(𝑎² + 𝑏²), where a and b are the lengths of the rectangle's sides.</p>
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<h2>Important Glossaries for Perimeter Including Diagonals</h2>
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<h2>Important Glossaries for Perimeter Including Diagonals</h2>
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<ul><li><strong>Perimeter:</strong>The total length of the sides of a shape.</li>
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<ul><li><strong>Perimeter:</strong>The total length of the sides of a shape.</li>
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</ul><ul><li><strong>Diagonal:</strong>A line connecting two non-adjacent vertices in a polygon.</li>
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</ul><ul><li><strong>Diagonal:</strong>A line connecting two non-adjacent vertices in a polygon.</li>
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</ul><ul><li><strong>Rectangle:</strong>A polygon with four sides and four right angles.</li>
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</ul><ul><li><strong>Rectangle:</strong>A polygon with four sides and four right angles.</li>
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</ul><ul><li><strong>Square:</strong>A polygon with four equal sides and four right angles.</li>
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</ul><ul><li><strong>Square:</strong>A polygon with four equal sides and four right angles.</li>
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</ul><ul><li><strong>Pythagorean Theorem:</strong>A mathematical formula used to find the length of the sides in a right-angled triangle, often used to calculate diagonals.</li>
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</ul><ul><li><strong>Pythagorean Theorem:</strong>A mathematical formula used to find the length of the sides in a right-angled triangle, often used to calculate diagonals.</li>
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</ul><p>What Is Measurement? 📏 | Easy Tricks, Units & 🎯 Fun Learning for Kids | ✨BrightCHAMPS Math</p>
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</ul><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>