9. Mensuration

9. Mensuration

  • 9

    Mensuration

    This section covers the concepts of mensuration, including the area and perimeter of various polygons, and the surface area and volume of solid shapes.

  • 9.1

    Introduction

    This section introduces the concepts of perimeter and area, as well as surface area and volume for various geometric shapes.

  • 9.2

    Area Of A Polygon

    This section covers methods to calculate the area of various polygons through decomposition into simpler shapes like triangles and trapeziums.

  • 9.3

    Solid Shapes

    This section introduces solid shapes, highlighting the differences between cuboidal, cubic, and cylindrical forms and their corresponding properties.

  • 9.4

    Surface Area Of Cube, Cuboid And Cylinder

    This section covers the determination of surface areas for cubes, cuboids, and cylinders, detailing the formulas and concepts necessary for computation.

  • 9.4.1

    Cuboid

    This section discusses the surface area of a cuboid, including its calculation and key properties.

  • 9.4.2

    Cube

    This section discusses the properties and calculations related to the surface area of a cube.

  • 9.4.3

    Cylinders

    This section focuses on the surface area of cylinders, exploring definitions, mathematical formulations, and practical applications.

  • 9.5

    Volume Of Cube, Cuboid And Cylinder

    This section explores the concept of volume as the amount of space occupied by three-dimensional objects, focusing on cubes, cuboids, and cylinders.

  • 9.5.1

    Cuboid

    This section explores how to calculate the volume of a cuboid by using the formula volume = length × breadth × height.

  • 9.5.2

    Cube

    This section presents the definition and volume formula of a cube, explaining its significance as a special type of cuboid.

  • 9.5.3

    Cylinder

    The section explains how to calculate the volume of a cylinder using its base area and height.

  • 9.6

    Volume And Capacity

    This section explores the concepts of volume and capacity, highlighting their definitions and the relationship between them.

    • Key Summary

    This chapter explores the concepts of mensuration, focusing on calculating the area and perimeter of various plane figures, including polygons and quadrilaterals. It also covers the surface area and volume of solid shapes such as cubes, cuboids, and cylinders, emphasizing practical applications through examples and exercises.

    Key Takeaways

    • The area of a polygon can be derived from the areas of its component triangles and trapeziums.
    • The surface area of three-dimensional shapes is the total area of all their faces.
    • Volume measures the space occupied by a three-dimensional object and is calculated differently for various solid shapes.

    Key Concepts

    • Area: The measure of the space covered by a two-dimensional shape, typically expressed in square units.
    • Perimeter: The total distance around the boundary of a two-dimensional shape.
    • Surface Area: The total area of the surface of a three-dimensional object.
    • Volume: The measure of the amount of space a three-dimensional object occupies, expressed in cubic units.
    • Cuboid: A three-dimensional shape with six rectangular faces.
    • Cylinder: A three-dimensional shape with two parallel circular bases connected by a curved surface.
    • Rhombus: A type of polygon that is a quadrilateral with opposite sides parallel and all sides equal in length.