Figures

Types of Figures in Geometry

Two common types of figures in geometry are:

1. Two-dimensional (2-D) figures; and

2. Three-dimensional (3-D) figures.

Two-dimensional Figures

A two-dimensional (or 2-D) figure is a flat or plane figure. These kinds of figures are called 2-D because they have just two dimensions, which are length and breadth. Examples of 2-D figures in geometry are squares, rectangles, circles and other Polygons. Take a look at the 2-D figures below.

Fig. 2. A Triangle; an example of a 2-dimensional figure.

Fig. 3. A circle; an example of a 2-dimensional figure.

You can tell that the figures above are two-dimensional because they are flat shapes on a surface having just length and breadth. You can check out our article on 2-dimensional figures to get more details.

Three-dimensional Figures

A three-dimensional (or 3-D) figure is a solid and tangible figure. It is tangible because it can be held or picked up. Unlike the 2-D, it's not just a plane figure on a surface. It has depth, volume, and thickness. It is called three-dimensional because it has length, breadth, and depth.

Some examples are cube, cuboid, cylinder, and cone. Some 3-dimensional figures are shown below.

Fig. 4. A cube; an example of a 3-dimensional figure.

Fig. 5. A cylindrical shape; an example of a 3-dimensional figure.

The first figure above is a cube figure and the second is a cylindrical figure. You can compare them and the 2-D figures. They do not only have length and breadth, but they also have depth and volume. They are solid figures, and they look like they can be picked up.

Open and Closed Figures in Geometry

Aside from figures being 2-D or 3-D, there are figures called open and closed in geometry.

These kinds of figures are not connected on both ends. It's like having a shape that has a missing part. The figures below are examples of open figures.

Fig. 6. An open figure.

Fig. 7. An open figure.

The shapes are either missing a line or a curve, which makes them open figures.

A closed figure is the opposite of an open figure. It's a complete and whole shape. Examples of closed figures in geometry are below.

Fig. 8. A closed square figure.

Fig. 9. A closed triangle figure.

Let's look at a quick example.

Significant Figures in Geometry

Significant figures are the basic or standard geometric figures. You come across these figures everyday around you. Examples are square, circle, triangle and rectangles.

Fig. 11. A square; an example of a significant figure.

Fig. 12. A Circle; an example of a significant figure.

Fig. 13. A Rectangle; an example of a significant figure.

Fig. 14. A Triangle; an example of a significant figure.

Composite Figures in Geometry

Imagine a single figure that can be split or separated into different geometric shapes. This kind of figure is called a composite figure.

You can tell by the name what it means because composite means containing multiple components and that is what a composite figure is.

Take a look at the composite figure below.

Fig. 15. A composite figure broken down into a rectangle and triangle.

The figure ABCD above is a trapezoid, but it can be separated into two figures. You can see that the trapezoid is made up of a rectangle and a triangle.

In the picture of a kite below, you can see that the figure can be split into two triangles.

Fig. 16. A composite figure broken down into two triangles.

In the L shape below, you can see that the figure can be split into a square and a rectangle.

Fig. 17. A composite figure broken down into a square and a rectangle.

All three of the above shapes are composite figures. If you observe closely, you will find out that many Polygons in geometry are composite figures.

You may come across a situation where you are asked to find the area or perimeter of a composite figure. To find the area of a composite figure, you will have to find the area of each shape that makes up the composite figure and add them together. This means that you will have to know the formula for finding the area of different shapes.

The same thing applies to finding the perimeter of a composite figure. You find the perimeter by adding the length of each side of the figure.

One of the main uses of composite figures is in determining area and perimeter. When you are asked to find the area or perimeter of a complex figure, you should consider it to be a composite figure. Look at the figure carefully to see the different shapes that it consists of. Find the area of each shape and add them together, or add the sides of every shape present in the case of finding a perimeter. Let's look at a short example.

Congruent and Similar Figures in Geometry

If a figure can be flipped or turned to form another figure, then the two figures are congruent.

Congruent figures should have corresponding sides and angles. If the figures are not identical in that way, then we can't call them congruent. Examples of congruent figures are below.

Fig. 21. A pair of congruent figures.

Fig. 22. A pair of congruent figures.

Take note of the second set of figures above. You might want to say that they are not congruent because they look different. But if you rotate the second one, you will see that it matches the first completely in shape and size.

If you want to identify congruent figures, look out for the edges, faces, volume, and even angles. If they are equal or corresponding, then they are congruent. Sometimes, lines are placed on the sides of figures to indicate whether they are congruent or not. See an example below.

Fig. 23. A pair of congruent triangles.

From the figure above, the sides of the triangles that have just one line are equal in length. The double line and the triple line also mean the same thing.

That means circles are especially easy to check. If two circles have the same radius then they are congruent!

What about similar figures?

If the only difference between two figures is size, then we can call them similar. They can have the same shape but are of different sizes.

Fig. 24. A pair of similar figures.

You can see from the above figures that one is smaller than the other. They look the same and are the same shape, but they are not equal in length, breadth, or volume. So, we call them similar but not congruent.

What about circles? Any two circles only really differ by their size, so all circles are similar!

A cube figure in geometry

Sometimes people can mistake a cube for a square, but there is a difference. A cube is a three-dimensional figure, while a square is a two-dimensional figure. In fact, a cube is made up of six squares! The figure below shows a cube and its different parts.

Fig. 25. The parts of a cube.

Below are some properties of a cube.

1. A cube has six square faces, eight vertices and twelve edges.

2. All the faces of a cube are equal.

3. The opposite faces of a cube are parallel to each other.

4. The opposite edges of a cube are parallel to each other.