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2026-01-01
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<p>Last updated on<strong>October 7, 2025</strong></p>
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<p>Last updated on<strong>October 7, 2025</strong></p>
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<p>The perimeter of a shape is the total length of its boundary. When dealing with combined shapes, the perimeter is obtained by summing the lengths of all the outer sides. Perimeter calculations are essential in various practical applications such as fencing a property, sewing, and more. In this topic, we will explore the perimeter of combined shapes.</p>
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<p>The perimeter of a shape is the total length of its boundary. When dealing with combined shapes, the perimeter is obtained by summing the lengths of all the outer sides. Perimeter calculations are essential in various practical applications such as fencing a property, sewing, and more. In this topic, we will explore the perimeter of combined shapes.</p>
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<h2>What is the Perimeter of Combined Shapes?</h2>
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<h2>What is the Perimeter of Combined Shapes?</h2>
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<p>The perimeter of combined shapes involves summing the lengths of all outer sides. By adding together the lengths of all sides that form the outer boundary, we obtain the perimeter of the combined shape.</p>
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<p>The perimeter of combined shapes involves summing the lengths of all outer sides. By adding together the lengths of all sides that form the outer boundary, we obtain the perimeter of the combined shape.</p>
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<p>For instance, consider a shape formed by combining a rectangle and a semicircle.</p>
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<p>For instance, consider a shape formed by combining a rectangle and a semicircle.</p>
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<p>If the rectangle has a length of 8 and a width of 4, and the semicircle has a diameter of 4, the perimeter includes the rectangle's perimeter minus the diameter, plus the semicircle's curved part.</p>
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<p>If the rectangle has a length of 8 and a width of 4, and the semicircle has a diameter of 4, the perimeter includes the rectangle's perimeter minus the diameter, plus the semicircle's curved part.</p>
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<h2>Formula for Perimeter of Combined Shapes</h2>
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<h2>Formula for Perimeter of Combined Shapes</h2>
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<p>Consider a shape formed by combining two rectangles. If the first rectangle has a length of 10 and width of 5, and the second rectangle has a length of 7 and width of 3, the perimeter would be:</p>
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<p>Consider a shape formed by combining two rectangles. If the first rectangle has a length of 10 and width of 5, and the second rectangle has a length of 7 and width of 3, the perimeter would be:</p>
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<p>Perimeter = (2×(10+5)) + (2×(7+3)) - 2×common length</p>
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<p>Perimeter = (2×(10+5)) + (2×(7+3)) - 2×common length</p>
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<p>This accounts for the shared side that doesn't contribute to the perimeter.</p>
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<p>This accounts for the shared side that doesn't contribute to the perimeter.</p>
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<h2>How to Calculate the Perimeter of Combined Shapes</h2>
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<h2>How to Calculate the Perimeter of Combined Shapes</h2>
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<p>To calculate the perimeter of combined shapes, apply the perimeter<a>formulas</a>for individual shapes, then adjust for shared or internal sides. For example, a shape combines a triangle with sides 6, 8, and 10, with a rectangle of length 6 and width 4.</p>
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<p>To calculate the perimeter of combined shapes, apply the perimeter<a>formulas</a>for individual shapes, then adjust for shared or internal sides. For example, a shape combines a triangle with sides 6, 8, and 10, with a rectangle of length 6 and width 4.</p>
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<p>The perimeter =<a>sum</a>of outer sides = 6 + 8 + 10 + 4 + 4.</p>
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<p>The perimeter =<a>sum</a>of outer sides = 6 + 8 + 10 + 4 + 4.</p>
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<p>Example Problem on Perimeter of Combined Shapes -</p>
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<p>Example Problem on Perimeter of Combined Shapes -</p>
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<p>A combined shape consists of a<a>square</a>with side 5 and a semicircle with a diameter of 5.</p>
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<p>A combined shape consists of a<a>square</a>with side 5 and a semicircle with a diameter of 5.</p>
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<p>The perimeter is calculated by: Perimeter = 4×5 + (π×(5/2)) - 5</p>
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<p>The perimeter is calculated by: Perimeter = 4×5 + (π×(5/2)) - 5</p>
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<p>Thus, the perimeter of the combined shape is approximately 30.7 units.</p>
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<p>Thus, the perimeter of the combined shape is approximately 30.7 units.</p>
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<h2>Tips and Tricks for Perimeter of Combined Shapes</h2>
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<h2>Tips and Tricks for Perimeter of Combined Shapes</h2>
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<p>Here are some helpful tips and tricks for calculating the perimeter of combined shapes:</p>
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<p>Here are some helpful tips and tricks for calculating the perimeter of combined shapes:</p>
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<p>1. Always remember to exclude any shared or internal sides in the calculation of the perimeter.</p>
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<p>1. Always remember to exclude any shared or internal sides in the calculation of the perimeter.</p>
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<p>2. When dealing with curves like semicircles, calculate the perimeter of the curved portion separately and add it to the linear parts. Use the formula: Curved part of a semicircle = π×radius.</p>
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<p>2. When dealing with curves like semicircles, calculate the perimeter of the curved portion separately and add it to the linear parts. Use the formula: Curved part of a semicircle = π×radius.</p>
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<p>3. Arrange the indicated side lengths of each individual shape clearly when calculating the perimeter of a group of shapes.</p>
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<p>3. Arrange the indicated side lengths of each individual shape clearly when calculating the perimeter of a group of shapes.</p>
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<p>4. Use precise and<a>constant</a>side lengths for practical applications like architecture and gardening to avoid errors.</p>
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<p>4. Use precise and<a>constant</a>side lengths for practical applications like architecture and gardening to avoid errors.</p>
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<p>5. If given the semi-perimeter in problems involving curves, remember it only pertains to the curved portion.</p>
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<p>5. If given the semi-perimeter in problems involving curves, remember it only pertains to the curved portion.</p>
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<h2>Common Mistakes and How to Avoid Them in Perimeter of Combined Shapes</h2>
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<h2>Common Mistakes and How to Avoid Them in Perimeter of Combined Shapes</h2>
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<p>While working with the perimeter of combined shapes, errors can occur. Here are solutions to common problems:</p>
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<p>While working with the perimeter of combined shapes, errors can occur. Here are solutions to common problems:</p>
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<h3>Problem 1</h3>
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<h3>Problem 1</h3>
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<p>A garden is designed in the shape of an L, with a long side of 12 meters, a short side of 6 meters, and a width of 3 meters. Find the perimeter of the garden.</p>
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<p>A garden is designed in the shape of an L, with a long side of 12 meters, a short side of 6 meters, and a width of 3 meters. Find the perimeter of the garden.</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 perimeter of the garden is 36 meters.</p>
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<p>The perimeter of the garden is 36 meters.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Consider the shape as two rectangles sharing a side: Perimeter = 12 + 6 + 3 + 3 + 6 + 6 = 36 meters.</p>
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<p>Consider the shape as two rectangles sharing a side: Perimeter = 12 + 6 + 3 + 3 + 6 + 6 = 36 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 path is created by combining a square with side 5 and a quarter circle with radius 5. Calculate the total perimeter.</p>
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<p>A path is created by combining a square with side 5 and a quarter circle with radius 5. Calculate the total perimeter.</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 total perimeter is approximately 26.57 units.</p>
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<p>The total perimeter is approximately 26.57 units.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Calculate the perimeter: Square = 4×5 = 20 Quarter circle = (π×5)/2</p>
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<p>Calculate the perimeter: Square = 4×5 = 20 Quarter circle = (π×5)/2</p>
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<p>Total perimeter = 20 + 7.85 - 5 = 26.57</p>
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<p>Total perimeter = 20 + 7.85 - 5 = 26.57</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 rectangle with length 8 cm and width 6 cm, combined with a semicircle of diameter 6 cm.</p>
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<p>Find the perimeter of a rectangle with length 8 cm and width 6 cm, combined with a semicircle of diameter 6 cm.</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>The perimeter is approximately 37.42 cm.</p>
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<p>The perimeter is approximately 37.42 cm.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Rectangle's perimeter: 2×(8+6) = 28</p>
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<p>Rectangle's perimeter: 2×(8+6) = 28</p>
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<p>Semicircle's curved part: (π×3) = 9.42</p>
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<p>Semicircle's curved part: (π×3) = 9.42</p>
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<p>Total perimeter: 28 + 9.42 - 6 = 37.42 cm</p>
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<p>Total perimeter: 28 + 9.42 - 6 = 37.42 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>Mia is creating a border around her flower bed, combining a triangle with sides 7, 9, and 11 meters with a rectangle of length 9 and width 3. What is the total perimeter?</p>
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<p>Mia is creating a border around her flower bed, combining a triangle with sides 7, 9, and 11 meters with a rectangle of length 9 and width 3. What is the total perimeter?</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 total perimeter is 41 meters.</p>
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<p>The total perimeter is 41 meters.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Calculate the perimeter: Triangle = 7 + 9 + 11 = 27</p>
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<p>Calculate the perimeter: Triangle = 7 + 9 + 11 = 27</p>
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<p>Rectangle = 2×(9+3) = 24</p>
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<p>Rectangle = 2×(9+3) = 24</p>
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<p>Subtract shared side: 24 - 9</p>
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<p>Subtract shared side: 24 - 9</p>
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<p>Total perimeter = 27 + 15 = 41 meters</p>
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<p>Total perimeter = 27 + 15 = 41 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>A playground has a shape formed by a rectangle of length 10 meters and width 5 meters, combined with a semicircle with a diameter of 5 meters. Find the perimeter.</p>
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<p>A playground has a shape formed by a rectangle of length 10 meters and width 5 meters, combined with a semicircle with a diameter of 5 meters. Find the perimeter.</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 perimeter is approximately 38.57 meters.</p>
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<p>The perimeter is approximately 38.57 meters.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Calculate the perimeter: Rectangle = 2×(10+5) = 30</p>
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<p>Calculate the perimeter: Rectangle = 2×(10+5) = 30</p>
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<p>Semicircle's curved part = (π×2.5) = 7.85</p>
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<p>Semicircle's curved part = (π×2.5) = 7.85</p>
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<p>Total perimeter = 30 + 7.85 - 5 = 38.57 meters</p>
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<p>Total perimeter = 30 + 7.85 - 5 = 38.57 meters</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 of Combined Shapes</h2>
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<h2>FAQs on Perimeter of Combined Shapes</h2>
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<h3>1.Evaluate the perimeter of a shape combining a rectangle of 6 cm by 4 cm and a semicircle of diameter 4 cm.</h3>
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<h3>1.Evaluate the perimeter of a shape combining a rectangle of 6 cm by 4 cm and a semicircle of diameter 4 cm.</h3>
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<p>Perimeter of rectangle = 2×(6+4) = 20</p>
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<p>Perimeter of rectangle = 2×(6+4) = 20</p>
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<p>Semicircle = (π×2)</p>
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<p>Semicircle = (π×2)</p>
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<p>Total perimeter = 20 + 6.28 - 4 = 22.28 cm</p>
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<p>Total perimeter = 20 + 6.28 - 4 = 22.28 cm</p>
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<h3>2.What is meant by the perimeter of combined shapes?</h3>
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<h3>2.What is meant by the perimeter of combined shapes?</h3>
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<p>The perimeter of combined shapes is the total length of the outer boundary of a shape formed by combining two or more basic shapes.</p>
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<p>The perimeter of combined shapes is the total length of the outer boundary of a shape formed by combining two or more basic shapes.</p>
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<h3>3.What are some basic shapes used in forming combined shapes?</h3>
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<h3>3.What are some basic shapes used in forming combined shapes?</h3>
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<p>Common basic shapes include rectangles, triangles, circles, squares, and semicircles.</p>
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<p>Common basic shapes include rectangles, triangles, circles, squares, and semicircles.</p>
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<h3>4.Which strategies help in calculating the perimeter of complex combined shapes?</h3>
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<h3>4.Which strategies help in calculating the perimeter of complex combined shapes?</h3>
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<p>Break down the shape into basic components, calculate each perimeter separately, and adjust for shared sides or internal parts.</p>
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<p>Break down the shape into basic components, calculate each perimeter separately, and adjust for shared sides or internal parts.</p>
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<h3>5.How do you handle curves in combined shapes?</h3>
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<h3>5.How do you handle curves in combined shapes?</h3>
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<p>Calculate the perimeter of curved sections separately using appropriate formulas, such as the circumference formula for circles or semicircles.</p>
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<p>Calculate the perimeter of curved sections separately using appropriate formulas, such as the circumference formula for circles or semicircles.</p>
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<h2>Important Glossaries for Perimeter of Combined Shapes</h2>
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<h2>Important Glossaries for Perimeter of Combined Shapes</h2>
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<ul><li><strong>Perimeter:</strong>The total length of the outer edges of a shape.</li>
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<ul><li><strong>Perimeter:</strong>The total length of the outer edges of a shape.</li>
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</ul><ul><li><strong>Combined Shape:</strong>A shape formed by combining two or more basic geometric shapes.</li>
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</ul><ul><li><strong>Combined Shape:</strong>A shape formed by combining two or more basic geometric shapes.</li>
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</ul><ul><li><strong>Semicircle:</strong>A half-circle, often contributing a curved part to a combined shape's perimeter.</li>
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</ul><ul><li><strong>Semicircle:</strong>A half-circle, often contributing a curved part to a combined shape's perimeter.</li>
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</ul><ul><li><strong>Shared Side:</strong>A side common to two shapes in a combined shape, often excluded in perimeter calculations.</li>
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</ul><ul><li><strong>Shared Side:</strong>A side common to two shapes in a combined shape, often excluded in perimeter calculations.</li>
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</ul><ul><li><strong>Curved Part:</strong>The non-linear portion of a shape's perimeter, such as an arc in a circle or semicircle.</li>
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</ul><ul><li><strong>Curved Part:</strong>The non-linear portion of a shape's perimeter, such as an arc in a circle or semicircle.</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>