{"id":836503,"date":"2024-07-13T12:42:38","date_gmt":"2024-07-13T07:12:38","guid":{"rendered":"https:\/\/leverageedu.com\/discover\/?p=836503"},"modified":"2024-07-13T12:42:38","modified_gmt":"2024-07-13T07:12:38","slug":"exam-prep-properties-of-rectangle","status":"publish","type":"post","link":"https:\/\/leverageedu.com\/discover\/indian-exams\/exam-prep-properties-of-rectangle\/","title":{"rendered":"Properties of Rectangle: A Complete Guide"},"content":{"rendered":"\n

Understanding the properties of rectangles unveils essential principles in geometry, where this quadrilateral can help you understand basic ideas and formulas. Defined by its four right angles and parallel sides of equal length, a rectangle is symmetry and efficiency. Terms such as length, width, diagonal, and perimeter are very important in describing its dimensions and characteristics. These properties not only support foundational geometric concepts but also find practical application in fields ranging from architecture and engineering to art and design. This comprehensive guide explores the basic details of properties of rectangles, encompassing their mathematical formulas, spatial relationships, and diverse applications, offering a full picture of this fundamental geometric shape.<\/p>\n\n\n\n\n\n\n

Definition of Rectangle<\/h2>\n\n\n\n

A rectangle is a planar shape that is two-dimensional and has four sides for each side. One definition of a rectangle is a polygon with four sides, in which the opposing sides are parallel to one another and equal to one another. It belongs to the category of quadrilaterals in which each of the four angles is either perpendicular to the other or equal to ninety degrees. As a specific kind of parallelogram, the rectangle is characterized by having all of its angles being equal. A square is a rectangle that has four sides that are also equal to one another.\u00a0<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

A rectangle is a four-sided polygon, or quadrilateral, with the following properties of Rectangle:<\/p>\n\n\n\n

    \n
  1. Four Right Angles<\/strong>: Each of the four interior angles is 90 degrees<\/strong>.<\/li>\n\n\n\n
  2. Opposite Sides are Equal and Parallel<\/strong>: The length of each pair of opposite sides is the same, and these sides are parallel to each other.<\/li>\n\n\n\n
  3. Diagonals are Equal<\/strong>: The diagonals (the lines connecting opposite corners) of a rectangle are equal in length.<\/li>\n\n\n\n
  4. Perimeter<\/strong>: The perimeter of a rectangle is the total distance around the shape, calculated as 2\u00d7(length+width)<\/strong>.<\/li>\n\n\n\n
  5. Area<\/strong>: The area of a rectangle is the amount of space it covers, found by multiplying the length by the width (Area=length\u00d7width<\/strong>).<\/li>\n<\/ol>\n\n\n\n

    Also Read: <\/strong>Find the Area of the Shaded Region<\/strong><\/a><\/p>\n\n\n\n

    Properties of Rectangle with Formulas<\/h2>\n\n\n\n

    A rectangle is a fundamental geometric shape characterized by its four right angles and parallel sides of equal length. Understanding its properties is crucial in various fields such as mathematics, architecture, and engineering. Below is a table summarizing the key properties of rectangle.<\/p>\n\n\n\n

    \"\"<\/figure>\n\n\n\n
    Property<\/strong><\/td>Description<\/strong><\/td><\/tr>
    Four Right Angles<\/strong><\/td>Each of the four interior angles is 90 degrees.<\/td><\/tr>
    Opposite Sides are Equal<\/strong><\/td>Opposite sides have the same length.<\/td><\/tr>
    Opposite Sides are Parallel<\/strong><\/td>Each pair of opposite sides is parallel.<\/td><\/tr>
    Diagonals are Equal<\/strong><\/td>The diagonals (lines connecting opposite corners) are equal in length.<\/td><\/tr>
    Diagonals Length<\/strong><\/td>D = \u221a(length\u00b2 + width\u00b2)<\/td><\/tr>
    Diagonals Bisect Each Other<\/strong><\/td>Each diagonal divides the rectangle into two equal triangles.<\/td><\/tr>
    Diagonals Form Isosceles Triangles<\/strong><\/td>When a diagonal is drawn, it forms two isosceles triangles within the rectangle.<\/td><\/tr>
    Perimeter<\/strong><\/td>The total distance around the rectangle, calculated as\u00a0 2\u00d7(length+width).<\/td><\/tr>
    Area<\/strong><\/td>The amount of space covered by the rectangle, calculated as\u00a0 length\u00d7width.<\/td><\/tr>
    Sum of Interior Angles<\/strong><\/td>The sum of all interior angles in a rectangle is 360 degrees.<\/td><\/tr>
    Symmetry<\/strong><\/td>A rectangle has two lines of symmetry (each line passes through the midpoints of opposite sides).<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

    Properties of Rectangle Solved Examples<\/h2>\n\n\n\n

    Here are 10 solved examples based on properties of rectangles, covering various aspects such as area, perimeter, and properties.<\/p>\n\n\n\n

    Q1:<\/strong> Find the area of a rectangle with a length of 8 units and a width of 5 units.<\/p>\n\n\n\n

    Solution:<\/strong> Area = length \u00d7 width\u00a0<\/p>\n\n\n\n

    = 8 \u00d7 5 = 40 square units.<\/p>\n\n\n\n

    Q2:<\/strong> Find the perimeter of a rectangle with a length of 12 units and a width of 7 units.<\/p>\n\n\n\n

    Solution:<\/strong> Perimeter = 2(length + width)\u00a0<\/p>\n\n\n\n

    = 2(12 + 7)\u00a0<\/p>\n\n\n\n

    = 2 \u00d7 19 = 38 units.<\/p>\n\n\n\n

    Q3:<\/strong> A rectangle has a length of 15 units and an area of 105 square units. Find the width.<\/p>\n\n\n\n

    Solution:<\/strong> Area = length \u00d7 width<\/p>\n\n\n\n

    therefore, width = Area \/ length\u00a0<\/p>\n\n\n\n

    = 105 \/ 15 = 7 units.<\/p>\n\n\n\n

    Q4:<\/strong> A rectangle has a width of 9 units and a perimeter of 52 units. Find the length.<\/p>\n\n\n\n

    Solution:<\/strong> Perimeter = 2(length + width)\u00a0<\/p>\n\n\n\n

    therefore, 52 = 2(length + 9).\u00a0<\/p>\n\n\n\n

    Solving for length: 52 \/ 2 = length + 9\u00a0<\/p>\n\n\n\n

    26 = length + 9;\u00a0<\/p>\n\n\n\n

    length = 26 \u2013 9 = 17 units.<\/p>\n\n\n\n

    Q5:<\/strong> Find the length of the diagonal of a rectangle with a length of 6 units and a width of 8 units.<\/p>\n\n\n\n

    Solution:<\/strong> Diagonal = \u221a(length\u00b2 + width\u00b2)\u00a0<\/p>\n\n\n\n

    = \u221a(6\u00b2 + 8\u00b2)\u00a0<\/p>\n\n\n\n

    = \u221a(36 + 64) = \u221a100 = 10 units.<\/p>\n\n\n\n

    Q6:<\/strong> A rectangular field has a length of 20 meters and a width of 15 meters. If the cost of fencing is $5 per meter, find the total cost.<\/p>\n\n\n\n

    Solution:<\/strong> Perimeter = 2(length + width)\u00a0<\/p>\n\n\n\n

    = 2(20 + 15)\u00a0<\/p>\n\n\n\n

    = 2 \u00d7 35 = 70 meters.\u00a0<\/p>\n\n\n\n

    Total cost = 70 \u00d7 5 = $350.<\/p>\n\n\n\n

    Q7:<\/strong> A rectangle has a perimeter of 48 units and a length of 14 units. Find the area.<\/p>\n\n\n\n

    Solution:<\/strong> Perimeter = 2(length + width)<\/p>\n\n\n\n

    therefore, 48 = 2(14 + width).\u00a0<\/p>\n\n\n\n

    Solving for width: 48 \/ 2 = 14 + width<\/p>\n\n\n\n

    24 = 14 + width;\u00a0<\/p>\n\n\n\n

    width = 24 \u2013 14 = 10 units.\u00a0<\/p>\n\n\n\n

    Area = length \u00d7 width\u00a0<\/p>\n\n\n\n

    = 14 \u00d7 10 = 140 square units.<\/p>\n\n\n\n

    Q8:<\/strong> A rectangle has a length of 5 units and a width of 3 units. If both dimensions are increased by 2 units, find the new area.<\/p>\n\n\n\n

    Solution:<\/strong> New length = 5 + 2 = 7 units<\/p>\n\n\n\n

    New width = 3 + 2 = 5 units.\u00a0<\/p>\n\n\n\n

    New area = 7 \u00d7 5 = 35 square units.<\/p>\n\n\n\n

    Q9:<\/strong> The length and width of a rectangle are in the ratio 4:3. If the perimeter is 56 units, find the dimensions.<\/p>\n\n\n\n

    Solution:<\/strong> Let length = 4x and width = 3x.\u00a0<\/p>\n\n\n\n

    Perimeter = 2(length + width)\u00a0<\/p>\n\n\n\n

    = 2(4x + 3x) = 2(7x) = 14x.\u00a0<\/p>\n\n\n\n

    Solving for x: 14x = 56<\/p>\n\n\n\n

    x = 56 \/ 14 = 4.\u00a0<\/p>\n\n\n\n

    Length = 4x = 4(4) = 16 units<\/p>\n\n\n\n

    Width = 3x = 3(4) = 12 units.<\/p>\n\n\n\n

    Q10:<\/strong> A rectangle has an area of 80 square units and a length of 10 units. Find the perimeter.<\/p>\n\n\n\n

    Solution:<\/strong> Area = length \u00d7 width<\/p>\n\n\n\n

    therefore, width = Area \/ length\u00a0<\/p>\n\n\n\n

    = 80 \/ 10 = 8 units.\u00a0<\/p>\n\n\n\n

    Perimeter = 2(length + width)\u00a0<\/p>\n\n\n\n

    = 2(10 + 8)\u00a0<\/p>\n\n\n\n

    = 2 \u00d7 18 = 36 units.<\/p>\n\n\n\n

    Also Read: <\/strong>Formula of Profit and Loss: Percentages<\/strong><\/a><\/p>\n\n\n\n

    FAQs<\/h2>\n\n\n\n
    What is the formula for Area of rectangle?<\/strong>

    Area of a rectangle = length \u00d7 width .<\/p> <\/div>

    How to prove a rectangle?<\/strong>

    Here are three simple ways to do it:\u00a01. Prove that all the angles are 90\u00b0.\u00a02. Prove that two opposite angles are 90\u00b0 and that one pair of sides is parallel.\u00a03. Prove that the diagonals cut each other in half and are all the same length.<\/p> <\/div>

    What is the principle of rectangle?<\/strong>

    Both sides of a rectangle are parallel and equal. Since a rectangle is like a parallelogram in every way, it is also called a parallelogram. The number of each of the rectangle\u2019s four inside angles is 90\u00b0, so they are all the same. All of a rectangle\u2019s inside sides add up to 360\u00b0.<\/p> <\/div> <\/div>\n\n\n\n

    RELATED BLOGS<\/strong><\/p>\n\n\n\n

    What are Vertices, Faces And Edges?<\/strong><\/a><\/td>Perimeter of Rectangle: Formula and Examples\u00a0<\/strong><\/a>
    <\/td><\/tr>
    Surface Area of Prism: Formula<\/strong><\/a><\/td>Area of Rectangle: Formula and Example\u00a0<\/strong><\/a>
    <\/td><\/tr>
    Surface Area of a Cuboid: Definition<\/strong><\/a><\/td>Different Maths Shapes for Students and Kids<\/strong><\/a><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

    This was all about \u201cProperties of Rectangle<\/strong>\u201d. For more such informative blogs, check out our Study Material Section<\/a>, or you can learn more about us by visiting our\u00a0 Indian exams<\/a> page.<\/p>\n","protected":false},"excerpt":{"rendered":"Understanding the properties of rectangles unveils essential principles in geometry, where this quadrilateral can help you understand basic…\n","protected":false},"author":115,"featured_media":836505,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"editor_notices":[],"footnotes":""},"categories":[369,476,396],"tags":[],"class_list":{"0":"post-836503","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-indian-exams","8":"category-maths","9":"category-study-material"},"yoast_head":"\nProperties of Rectangle: A Complete Guide - Leverage Edu Discover<\/title>\n<meta name=\"description\" content=\"Read this article on Properties of Rectangle.Learn more about properties of rectangle in detial .Let's start!\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/leverageedu.com\/discover\/indian-exams\/exam-prep-properties-of-rectangle\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Properties of Rectangle: A Complete Guide\" \/>\n<meta property=\"og:description\" content=\"Read this article on Properties of Rectangle.Learn more about properties of rectangle in detial .Let's start!\" \/>\n<meta property=\"og:url\" content=\"https:\/\/leverageedu.com\/discover\/indian-exams\/exam-prep-properties-of-rectangle\/\" \/>\n<meta property=\"og:site_name\" content=\"Leverage Edu Discover\" \/>\n<meta property=\"article:published_time\" content=\"2024-07-13T07:12:38+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/blogassets.leverageedu.com\/media\/uploads\/sites\/9\/2024\/07\/15073737\/Properties-of-Rectangle.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"1024\" \/>\n\t<meta property=\"og:image:height\" content=\"640\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"author\" content=\"Mohit Rajak\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Mohit Rajak\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"5 minutes\" \/>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"Properties of Rectangle: A Complete Guide - 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Prove that all the angles are 90\u00b0.\u00a0<br\/>2. Prove that two opposite angles are 90\u00b0 and that one pair of sides is parallel.\u00a0<br\/>3. Prove that the diagonals cut each other in half and are all the same length.<br\/>","inLanguage":"en-US"},"inLanguage":"en-US"},{"@type":"Question","@id":"https:\/\/leverageedu.com\/discover\/indian-exams\/exam-prep-properties-of-rectangle\/#faq-question-1720854558815","position":3,"url":"https:\/\/leverageedu.com\/discover\/indian-exams\/exam-prep-properties-of-rectangle\/#faq-question-1720854558815","name":"What is the principle of rectangle?","answerCount":1,"acceptedAnswer":{"@type":"Answer","text":"Both sides of a rectangle are parallel and equal. Since a rectangle is like a parallelogram in every way, it is also called a parallelogram. The number of each of the rectangle's four inside angles is 90\u00b0, so they are all the same. All of a rectangle's inside sides add up to 360\u00b0.","inLanguage":"en-US"},"inLanguage":"en-US"}]}},"acf":[],"_links":{"self":[{"href":"https:\/\/leverageedu.com\/discover\/wp-json\/wp\/v2\/posts\/836503","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/leverageedu.com\/discover\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/leverageedu.com\/discover\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/leverageedu.com\/discover\/wp-json\/wp\/v2\/users\/115"}],"replies":[{"embeddable":true,"href":"https:\/\/leverageedu.com\/discover\/wp-json\/wp\/v2\/comments?post=836503"}],"version-history":[{"count":0,"href":"https:\/\/leverageedu.com\/discover\/wp-json\/wp\/v2\/posts\/836503\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/leverageedu.com\/discover\/wp-json\/wp\/v2\/media\/836505"}],"wp:attachment":[{"href":"https:\/\/leverageedu.com\/discover\/wp-json\/wp\/v2\/media?parent=836503"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/leverageedu.com\/discover\/wp-json\/wp\/v2\/categories?post=836503"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/leverageedu.com\/discover\/wp-json\/wp\/v2\/tags?post=836503"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}