{"id":9906,"date":"2026-07-03T17:39:42","date_gmt":"2026-07-03T17:39:42","guid":{"rendered":"https:\/\/kapdec.com\/help\/?p=9906"},"modified":"2026-07-03T17:39:42","modified_gmt":"2026-07-03T17:39:42","slug":"area-trapezium-and-parallelogram","status":"publish","type":"post","link":"https:\/\/kapdec.com\/help\/area-trapezium-and-parallelogram\/","title":{"rendered":"Area Trapezium And Parallelogram"},"content":{"rendered":"
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KAPDEC® | Elite STEM Learning Platform | https:\/\/kapdec.com<\/a><\/p>\n

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Unit: <\/strong>Area Of Shapes<\/strong><\/h2>\n

Chapter: <\/strong>Area of Trapezium & Parallelogram<\/strong><\/h3>\n

Reference: – What is Area, Area of a Parallelogram (Formula and Derivation), Area of a Trapezium (Formula and Derivation), Finding Base or Height from Area, Real-Life Applications, Solved Examples, Odd-One-Out Problems, Common Mistakes<\/em><\/p>\n

After studying this chapter, you should be able to understand:<\/strong><\/p>\n

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  • How to Find the Area of a Parallelogram<\/em><\/li>\n
  • How to Find the Area of a Trapezium (Trapezoid)<\/em><\/li>\n
  • How to Find Missing Dimensions Given Area<\/em><\/li>\n
  • Difference Between Area Formulas of Different Shapes<\/em><\/li>\n<\/ul>\n

    Introduction to Area of Trapezium & Parallelogram<\/strong><\/p>\n

    Definition<\/u><\/strong><\/p>\n

    Area is the amount of space enclosed within a two-dimensional shape, measured in square units (cm², m², in², etc.). A parallelogram is a quadrilateral with two pairs of parallel sides. A trapezium (called trapezoid in the US) is a quadrilateral with exactly one pair of parallel sides.<\/p>\n

    When we calculate area, we essentially ask:<\/p>\n

    "How many square units can fit inside this shape?"<\/p>\n

    Once we know the formulas, we can find area quickly without counting squares.<\/p>\n

    Importance of Area<\/u><\/strong><\/p>\n

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    • Used in construction (flooring, painting, roofing)<\/li>\n
    • Essential for land measurement and agriculture<\/li>\n
    • Helps in designing and manufacturing products<\/li>\n
    • Foundation for volume and surface area in higher grades<\/li>\n<\/ul>\n

      Example<\/u><\/strong><\/p>\n

      The area of a parallelogram with base 10 cm and height 5 cm is 50 cm². The area of a trapezium with bases 8 cm and 12 cm and height 4 cm is 40 cm².<\/p>\n

      Subtopics<\/u><\/strong><\/p>\n

      1. Area of a Parallelogram<\/strong><\/p>\n

      A parallelogram is a quadrilateral with opposite sides parallel and equal.<\/p>\n

      Formula: Area = base × height (A = b × h)<\/p>\n

      Important: The height (h) is the perpendicular distance between the bases, NOT the length of the slanted side.<\/p>\n

      Derivation: A parallelogram can be transformed into a rectangle by cutting off a right triangle from one end and moving it to the other end. The rectangle has length = base and width = height, so area = b × h.<\/p>\n

      Example 1:<\/strong> Parallelogram with base 8 cm and height 5 cm
      \nArea = 8 × 5 = 40 cm²<\/p>\n

      Example 2:<\/strong> Parallelogram with base 12 m and height 7 m
      \nArea = 12 × 7 = 84 m²<\/p>\n

      Finding Base or Height:<\/strong> If area is known, base = Area ÷ height, height = Area ÷ base<\/p>\n

      Example – Find height:<\/strong> Area = 45 cm², base = 9 cm → height = 45 ÷ 9 = 5 cm<\/p>\n

      2. Area of a Trapezium (Trapezoid)<\/strong><\/p>\n

      A trapezium is a quadrilateral with exactly one pair of parallel sides. The parallel sides are called bases (a and b). The perpendicular distance between them is the height (h).<\/p>\n

      Formula:<\/strong> Area = (1\/2) × (sum of parallel sides) × height<\/p>\n

      A = (1\/2) × (a + b) × h<\/p>\n

      Derivation:<\/strong> A trapezium can be divided into a parallelogram and a triangle, or two triangles, or seen as half of a parallelogram with the same height and base equal to (a + b).<\/p>\n

      Example 1:<\/strong> Bases = 6 cm and 10 cm, height = 4 cm
      \nArea = (1\/2) × (6 + 10) × 4 = (1\/2) × 16 × 4 = 8 × 4 = 32 cm²<\/p>\n

      Example 2:<\/strong> Bases = 5 m and 9 m, height = 6 m
      \nArea = (1\/2) × (5 + 9) × 6 = (1\/2) × 14 × 6 = 7 × 6 = 42 m²<\/p>\n

      Finding a Base or Height:<\/strong> If area is known, (a + b) = (2 × Area) ÷ h, or h = (2 × Area) ÷ (a + b)<\/p>\n

      Example – Find missing base:<\/strong> Area = 50 cm², one base = 8 cm, height = 5 cm
      \n(a + b) = (2 × 50) ÷ 5 = 100 ÷ 5 = 20 → b = 20 – 8 = 12 cm<\/p>\n

      Solved Examples<\/u><\/strong><\/p>\n

      Example 1 – Area of Parallelogram:<\/strong> Find the area of a parallelogram with base 15 cm and height 8 cm.<\/p>\n

      Solution:<\/strong> A = 15 × 8 = 120 cm²<\/p>\n

      Answer:<\/strong> 120 cm²<\/p>\n

       <\/p>\n

      Example 2 – Height of Parallelogram:<\/strong> A parallelogram has area 72 m² and base 12 m. Find its height.<\/p>\n

      Solution:<\/strong> height = Area ÷ base = 72 ÷ 12 = 6 m<\/p>\n

      Answer:<\/strong> 6 m<\/p>\n

       <\/p>\n

      Example 3 – Area of Trapezium:<\/strong> Find the area of a trapezium with parallel sides 7 cm and 13 cm and height 5 cm.<\/p>\n

      Solution:<\/strong> A = (1\/2) × (7 + 13) × 5 = (1\/2) × 20 × 5 = 10 × 5 = 50 cm²<\/p>\n

      Answer:<\/strong> 50 cm²<\/p>\n

       <\/p>\n

      Example 4 – Missing Base of Trapezium:<\/strong> A trapezium has area 84 m², height 7 m, and one base 10 m. Find the other base.<\/p>\n

      Solution:<\/strong> (a + b) = (2 × 84) ÷ 7 = 168 ÷ 7 = 24 → b = 24 – 10 = 14 m<\/p>\n

      Answer:<\/strong> 14 m<\/p>\n

      Common Mistakes to Avoid<\/u><\/strong><\/p>\n

      Mistake 1 – Using the slanted side as height in a parallelogram<\/strong>
      \nThe height must be perpendicular to the base, not the length of the slanted side.
      \nCorrect understanding: height is the shortest distance between the bases.<\/p>\n

      Mistake 2 – Forgetting the 1\/2 in trapezium formula<\/strong>
      \nArea = (1\/2)(a+b)h, not (a+b)h. Without 1\/2, the area would be twice the correct value.
      \nCorrect understanding: Always include the 1\/2 factor for trapezium.<\/p>\n

      Mistake 3 – Confusing the two bases in trapezium<\/strong>
      \nThe two parallel sides are both bases. The order does not matter because addition is commutative.
      \nCorrect understanding: a + b = b + a, so no need to worry which base is which.<\/p>\n

      Mistake 4 – Using the legs of trapezium as height<\/strong>
      \nThe legs (non-parallel sides) are not the height unless perpendicular to the bases.
      \nCorrect understanding: Height is the perpendicular distance between the parallel sides.<\/p>\n

      Mistake 5 – Mixing up trapezium and parallelogram formulas<\/strong>
      \nParallelogram: A = b × h (no 1\/2), Trapezium: A = (1\/2)(a+b)h (has 1\/2 and two bases).
      \nCorrect understanding: Memorize both formulas and know when to use each.<\/p>\n

      Mistake 6 – Forgetting to use consistent units<\/strong>
      \nIf base is in meters and height in centimeters, the area will be incorrect.
      \nCorrect understanding: Convert both dimensions to the same unit before multiplying.<\/p>\n

      Quick Reference Summary<\/u><\/strong><\/p>\n

      Parallelogram Area:<\/strong> A = b × h
      \nb = length of base, h = perpendicular height<\/p>\n

      Trapezium Area:<\/strong> A = (1\/2) × (a + b) × h
      \na and b = lengths of parallel sides, h = perpendicular height<\/p>\n

      Parallelogram – Opposite sides parallel and equal, height perpendicular to base<\/strong><\/p>\n

      Trapezium – Exactly one pair of parallel sides, height perpendicular distance between them<\/strong><\/p>\n

      To Find Missing Dimension:<\/strong>
      \nParallelogram: b = A ÷ h, h = A ÷ b
      \nTrapezium: (a+b) = 2A ÷ h, h = 2A ÷ (a+b)<\/p>\n

      Units:<\/strong> Area is always in square units (cm², m², in², ft², etc.)<\/p>\n

       <\/p>\n

      <\/p>\n