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Mathematics

Gr 6 Properties of

2D and 3D Shapes

Explanations, illustrations

and exercises.

Content:

• Definitions and terminology of 2D Shapes

• Properties of 2D Shapes

• Definitions and terminology of 3D Shapes

• Properties of 3D Shapes

• Polygons

• Types of Angles

• The Circle

• Nets of 3D Shapes

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2D Shapes

Definition

2D Shape: is a flat surface with only two dimensions namely length and width.

Recognizing shapes by their sides:

Curved sides

Straight sides

Curved and straight sides

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Properties of 2-D Shapes

Shape Object Properties

Square -All four sides are the same

length.

-All 4 angles are equal. -All angles are 90°.

-The opposite sides are parallel.

Rectangle -Two pairs of opposite sides are equal.

-All 4 angles are equal. -All angles are 90°

Circle

-Curved edges -No straight sides

-No angles

Triangle

-Three sides

Equilateral

triangle

-Three sides are the same

length. -All three angles are 60°.

All three angles are equal.

Isosceles triangle

-Two sides (legs) are the same

length. -Two angles are equal.

Scalene triangle

-No equal sides.

-90° angle.

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Kite

-Two equally adjacent sides.

Trapezium

-One pair parallel opposite sides .

Parallelogram -Two pairs equal opposite sides.

-Two pairs parallel opposite

sides.

Rhombus -Four equally long sides. -Two opposite sides are

parallel.

-Two pair of angles are equally sized.

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Polygons:

2D shapes with just straight sides are called polygons and we group them

according to:

• The number of sides

• Length of the sides

• Sizes of the angles in the shapes

Shape Name Number of angles and

sides

Triangle 3 angles and 3 sides

Square/Quadrilateral 4 angles and 4 sides

Pentagon

5 angles and 5 sides

Hexagon 6 angles and 6 sides

Heptagon 7 angles and 7 sides

Octagon

8 angles and 8 sides

Decagon 10 angles and 10 sides

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Angles:

Angle: An angle is formed where two lines meet eg.

Vertex: the corner where the two lines meet.

Vertex

Types of angles:

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The Circle:

3D Shapes

Definition

3D objects take up space, this is length, width and height.

Properties of 3D Shapes

vertex

edge

face

Important:

Face: is the flat surface of a 3D shape.

Edges: Where two faces meet.

Vertices: the point where 3 or more edges meet.

Base: The surface of the object.

Angle: is formed were two lines meet.

Chord

Diameter

Centre

Radius

Arch

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Object

Name of object

Num

ber

of f

aces

Num

ber

of f

lat

surf

aces

Num

ber

of c

urve

d

face

s

Num

ber

of e

dge

s

Num

ber

of

vert

ices

Rectangular

prism 5 5 0 9 6

Cylinder

3 2 1 2 0

Sphere

1 0 1 0 0

Cone

2 1 1 1 1

Cube

6 6 0 12 8

Rectangular prism

6 6 0 12 8

Pyramid

5 5 0 8 5

Tetrahedron/

Pyramid with all

faces triangles.

4 4 0 6 4

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3D Object

height

width

Length

Tetra means 4, thus a Tetrahedron has 4 faces and all of them are Triangles

(Triangular pyramid)

A Square based pyramid has 5 faces, one is a Square and the other 4 are

Triangles.

Prisms: It is a 3-D shape with two identical, faces that are polygons.

• It has only flat faces.

• 2 identical faces.

• Other faces are rectangles except for a cube which as 6 squares.

• Gets its name from the two identical faces.

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Special prisms: Cube - a Cube has 6 faces that are all squares.

Pyramids: Are 3D objects with a polygon base and the other faces are all

Triangles.

• Side faces are always Triangles.

• Sides all meet at one point called and APEX.

• The base always consists of a polygon.

• It gets its name from the base.

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Net’s of 3D Shapes

The net of an object is the outline when an object is folded open. It is the plan

of the object.

1. Cube 2. Cylinder

3. Rectangular prism 4. Cone

5. Triangular prism 6. Tetrahedron

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Cone

Cone Hexagonal

prism

Cylinder

Rectangular

prism

Tetrahedron

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Exercise 1

1. Give the name of the following 2-D shapes below:

1.1)

________________

1.2)

__________________

1.3)

________________________

1.4)

_______________________

1.5)

____________________

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2. Draw the following shapes:

2.1) Kite 2.2) Rectangle

2.3) Pentagon 2.4) Parallelogram

3.) Say whether the following statements are TRUE or FALSE:

3.1) An Octagon is a shape with 7 faces? ______________

3.2) ‘A Circle has two right angles?? ______________

3.3) A Polygon is A shape with 4 faces? ______________

3.4) A Square has 4 angles that are the same size? ____________

4. Draw the following angles:

4.1) Right angle 4.2) Obtuse angle

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4.3) Acute angle 4.4) Straight angle

5. Identify the following angles:

5.1)

______________

5.2)

_____________________

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Exercise 2

1. What is a 3D shape?

_________________________________________________________________

2. What is a face?

_________________________________________________________________

3. What is a vertex?

_________________________________________________________________

4. Wat is a edge?

_________________________________________________________________

5. Complete the table:

Name of the 3D

object Number of faces

Number of

vertices Number of edges

Cone

Cylinder

Cube

Square base

pyramid

Rectangular

prism

Triangular prism

Sphere

Tetrahedron

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Exercise 3

1. Give the names of the 3-D objects below:

____________________ _________________ _____________________

____________________ _________________ _____________________

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Exercise 4

1. Give the names of the nets of 3D shapes:

2. Answer the following questions:

2.1) Which shape has 4 faces, 6edges and 4 vertices: __________________

2.2) Which shape has 6 equal faces: ___________________

2.3) Which shape has 5 faces, 9edges and 6 vertices:__________________

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Exercise 5

1. Label the circle:

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Exercise 6

Cut out the nets of the 3D shapes and build them.

Cube:

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Rectangular prism

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Triangular prism

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Cone

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Cylinder

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Pyramid

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Tetrahedron