So far we have worked with common two-dimensional figures such as the square or the triangle. Three-dimensional figures are those that extend into the third dimension, meaning that in addition to length and width, they also have height (that is, the figure has depth).

What differences do three-dimensional figures have?

Three-dimensional figures have several definitions that we will see next: Below is a three-dimensional figure that we will use to learn each definition - The cube:

Face: it is the flat side of a three-dimensional figure In the cube we have here, there are 6 faces (one of them is painted gray) Edge: these are the lines that connect one face to another in a three-dimensional figure In the cube we have here, there are 12 edges (painted green) Vertex: it is the point that connects the edges In the cube we have here, there are 8 vertices (painted orange)

Volume: it is the amount of space contained within a three-dimensional figure. The units of measurement are $cm^3$ .

The cuboid is a three-dimensional figure composed of 6 rectangles.

Each cuboid has:

6 faces: the rectangles that make up the cuboid - three pairs of rectangles that can be different from each other. 12 edges: the edges of the cuboid (divided into length, width, and height) - marked in green 8 vertices: the points where the edges meet - marked in orange

It is the sum of the area of the four lateral rectangles (without the bases). The lateral area of a cuboid can be calculated with the following formula: a- Length b- Width h- Height

The cylinder is a three-dimensional figure composed of two identical parallel circles called bases, between which the lateral area expands.

Other properties:

The distance between the two bases is constant and is called the height of the cylinder - we will mark it with an $H$ The radius of both bases is equal, we will mark it with an $R$

Volume of the cylinder

The volume contained within the cylinder is usually denoted by $V$. Formula to calculate the volume of the cylinder: $π\times \R^2\times \H = V$

When:

$π$ = PI ($3.14$) $R$ = Radius of the base $H$ = Height of the cylinder

Let's practice! In a right triangular prism, are the triangular bases always identical? Solution: Yes! The triangles, which are actually the bases, are always the same. Exercise: How many heights are there in a right triangular prism? Are they identical? Solution: There are 3 heights in a right triangular prism and they always have the same length. Exercise: Do the three rectangles that make up the lateral faces of the prism have to be identical? Solution: No. The edges of the triangle do not necessarily have to be equal and this could create different rectangles.

Volume of the right triangular prism

The volume of the prism is usually expressed through the following formula: $V= S \cdot H$

The area of a right triangular prism is, in fact, the total sum of the surfaces of its two bases (the triangles) and its three lateral faces (the rectangles).