Prisms and Pyramids

This page focuses on the formulas for prisms and pyramids, providing a comprehensive formulario geometria solida pdf. It covers various aspects of these 3D shapes, including surface area, volume, and other key measurements.

The page begins with the same important note as before, emphasizing that all lengths must be in the same unit of measurement for accurate calculations.

The shapes covered include:

1. Prism $general$
2. Rectangular Parallelepiped
3. Cube
4. Pyramid $general$
5. Right Pyramid
6. Arbitrary Pyramid
7. Truncated Pyramid

For each shape, the page provides formulas for lateral surface area $S₁$, total surface area $St$, volume $V$, and in some cases, diagonal length $d$.

Definition: A prism is a 3D shape with two identical ends $bases$ and flat sides.

Example: For a cube, all formulas are expressed in terms of the side length s. The volume is simply V = s³.

Highlight: The page includes formulas for both regular pyramids and truncated pyramids, which are less commonly found in basic geometry resources.

The bottom of the page includes a legend explaining the symbols used in the formulas, such as h for height, s for edge length, and 2p for perimeter.

This page serves as an excellent reference for students studying solid geometry or professionals working with 3D shapes in fields like engineering or architecture.

Solids of Rotation

This page focuses on solidi di rotazione, providing comprehensive formulas for various shapes created by rotating 2D figures around an axis. It serves as an excellent resource for those wondering "Come si calcola il volume dei solidi di rotazione?" and "Come si ottengono i solidi di rotazione?"

The solids covered on this page include:

1. Cylinder
2. Cone
3. Truncated Cone
4. Sphere

For each shape, the page provides formulas for lateral surface area $S₁$, total surface area $St$, base area $Sb$, and volume $V$. Additionally, it includes formulas to calculate various dimensions when other measurements are known.

Definition: Solids of rotation are 3D objects formed by rotating a 2D shape around an axis.

Example: For a cylinder, the lateral surface area is given by S₁ = 2πrh, where r is the radius and h is the height.

Highlight: The page includes formulas for truncated cones, which are less commonly found in basic geometry resources but are important in many practical applications.

Vocabulary: "Apotema" $apothem in English$ appears in some formulas, referring to the slant height of a cone or pyramid.

The bottom of the page includes a legend explaining the symbols used in the formulas, such as h for height, r for radius, and π for pi $approximately 3.14$.

This page is particularly useful for students studying advanced geometry or professionals in fields like engineering or computer graphics who need to work with rotational solids.

Regular Polyhedra

This final page focuses on regular polyhedra, also known as Platonic solids. It provides formulas for surface area, volume, and height of these unique 3D shapes, serving as a specialized formulario di geometria piana da stampare.

The regular polyhedra covered are:

1. Tetrahedron $4 triangular faces$
2. Cube or Hexahedron $6 square faces$
3. Octahedron $8 triangular faces$
4. Dodecahedron $12 pentagonal faces$
5. Icosahedron $20 triangular faces$

For each polyhedron, the page provides formulas for total surface area $S$ and volume $V$ in terms of the edge length $s$. It also includes the number of faces, vertices, and edges for each shape.

Definition: Regular polyhedra are three-dimensional solids whose faces are all congruent regular polygons.

Example: For a tetrahedron, the surface area is given by S = s²√3, and the volume by V = $s³√2$/12.

Highlight: The page includes Euler's formula $f + v = s + 2$ for polyhedra, where f is the number of faces, v is the number of vertices, and s is the number of edges.

Vocabulary: "Spigolo" $edge in English$ is a key term used throughout this page, referring to the line segment where two faces of a polyhedron meet.

The bottom of the page includes a legend explaining the symbols used in the formulas, such as h for height and s for edge length.

This page is particularly valuable for students studying advanced geometry or professionals in fields like crystallography or 3D modeling who need to work with these complex shapes.

Area and Perimeter of Plane Figures

This page provides essential formule area e perimetro figure piane pdf for various 2D shapes. It serves as a comprehensive formulario geometria piana pdf for students and professionals alike.

The page begins with a crucial note that all lengths must be expressed in the same unit of measurement when using these formulas. This ensures accuracy in calculations.

The shapes covered include:

1. Triangle
2. Parallelogram
3. Rectangle
4. Square
5. Rhombus
6. Trapezoid
7. Circle
8. Ellipse

For each shape, the page provides formulas for both perimeter and area. In some cases, additional formulas for diagonal lengths or other relevant measurements are included.

Highlight: The triangle section includes both the standard area formula $A = ½bh$ and Heron's formula for calculating area using side lengths.

Example: For a square, the perimeter is given by 2p = 4l, where l is the side length, and the area is simply A = l².

Vocabulary: The term "apothem" $apotema in Italian$ appears in some formulas, referring to the distance from the center of a regular polygon to the midpoint of any side.

This page serves as an excellent quick reference guide for students studying geometry or anyone needing to quickly recall formulas for common plane figures.