1.3 Surface area of 3-dimensional shapes

This chapter talks about line symmetry, rotational symmetry and transformations, and surface area of 3-dimensional shapes. We will learn how to find the lines of symmetry in 2-dimensional shapes, and whether a 2-dimensional shape has rotational symmetry. Also, we will learn how symmetry can help us find surface area of 3-dimensional shapes.

Symmetry can be found all around us. The fact that we are learning symmetry now is because our ancestors were so amazed by the symmetry in nature that a stream of study was developed!

A line of symmetry is a line that divides an object into two and produces two mirror images of each other. The lines of symmetry can be in any directions: horizontal, vertical or diagonal. An object can have more than one line of symmetry. The number of lines of symmetry varies in different polygons.

In the second part of the lesson, we will then explore rotational symmetry in 2-dimensional shapes. To say a figure has rotational symmetry means that when this figure turns about its centre of rotation, it will still look the same after a certain amount of rotation. Different shapes have different order of rotation and angle of rotation. Order of rotation refers to the number of times that the figure looks the same in one complete turn; while the angle of rotation is the smallest angle that the figure needs to turn so that it still looks the same. Like the line of symmetry, the order and angle of rotation can be different in different polygons too. For example, a regular hexagon has an order of rotation of 6 and its angle of rotation is 60°.

The last part of this lesson focuses on how to find the surface area of 3-dimensional shapes. Surface area is the total area of all faces of a shape. Thanks to our ancient mathematicians, we have formulas to help us find surface areas of many regular objects.

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Surface area of 3-dimensional shapes

In this section, we will learn how to calculate the surface area of 3D objects. We will also look further into the subject ? What would happen to the surface area if the shapes are cut into pieces? How about a piece is cut out of the shape?


    • a)
      What are the dimensions of the cutout piece?
    • b)
      How does the surface area of the original rectangular object change after cutting out the corner piece?
  • 2.
    Below is a rectangular object formed by six blocks which all have the same size.

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Surface area of 3-dimensional shapes

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