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Illustration of a plane passing through a prismatoid.

Plane Passing Through Prismatoid

Illustration of a plane passing through a prismatoid.

Illustration to show how volume of a prismatoid is found. "The volume of a prismatoid is equal to the product of one sixth of its altitude into the sum of its bases and four times its mid-section." V=1/6H(B+b+4M)

Prismatoid Illustration for Volume

Illustration to show how volume of a prismatoid is found. "The volume of a prismatoid is equal to the…

Illustration of 2 right octagonal prisms with congruent bases, but different heights. The height of the smaller prism is one half that of the larger.

2 Octagonal Prisms

Illustration of 2 right octagonal prisms with congruent bases, but different heights. The height of…

Illustration of 2 right rectangular prisms. The bases are congruent, but the height of the smaller prism is one half that of the larger. Hidden edges are shown.

2 Rectangular Prisms

Illustration of 2 right rectangular prisms. The bases are congruent, but the height of the smaller prism…

Illustration of 2 right rectangular prisms. The bases are congruent, but the height of the smaller prism is one half that of the larger.

2 Rectangular Prisms

Illustration of 2 right rectangular prisms. The bases are congruent, but the height of the smaller prism…

Illustration of 2 Similar right octagonal prisms. The height and length of the edges of the smaller prism are one half that of the larger.

2 Similar Octagonal Prisms

Illustration of 2 Similar right octagonal prisms. The height and length of the edges of the smaller…

Illustration of 4 congruent rectangular prisms placed in the shape of a square. They are arranged to look like they are 3-dimensional rectangular solids coming out of the page.

4 Congruent Rectangular Prisms

Illustration of 4 congruent rectangular prisms placed in the shape of a square. They are arranged to…

A cluster of 4 right hexagonal prisms with congruent bases, but varying heights.

4 Hexagonal Prisms

A cluster of 4 right hexagonal prisms with congruent bases, but varying heights.

Illustration showing two prisms are equal if the three faces which include a trihedral angle of the one are respectively equal to three faces which include a trihedral angle of the other, and are similarly placed.

Equal Prisms

Illustration showing two prisms are equal if the three faces which include a trihedral angle of the…

Illustration of 2 parallelopipeds/rectangular prisms.

Rectangular prisms

Illustration of 2 parallelopipeds/rectangular prisms.

Illustration of 3 parallelopipeds/rectangular prisms.

Rectangular prisms

Illustration of 3 parallelopipeds/rectangular prisms.

Illustration of 2 rectangular prism used to show volume.

Rectangular Prisms Showing Volume

Illustration of 2 rectangular prism used to show volume.

Illustration of 2 similar right decagonal prisms. Both have regular decagons for bases and rectangular faces. The height of the prism and length of the side of the decagon on the smaller decagonal prism are one half that of the larger.

Similar Decagonal Prisms

Illustration of 2 similar right decagonal prisms. Both have regular decagons for bases and rectangular…

Illustration of 2 similar right heptagonal/septagonal prisms. Both have regular heptagons/septagons for bases and rectangular faces. The height of the prism and length of the side of the heptagon on the smaller heptagonal prism are one half that of the larger.

Similar Heptagonal/Septagonal Prisms

Illustration of 2 similar right heptagonal/septagonal prisms. Both have regular heptagons/septagons…

Illustration of 2 similar right hexagonal prisms. The height of the prism and length of the side of the hexagon on the smaller hexagonal prism are one half that of the larger.

Similar Hexagonal Prisms

Illustration of 2 similar right hexagonal prisms. The height of the prism and length of the side of…

Illustration of 2 similar right hexagonal prisms. The height of the prism and length of the side of the hexagon on the smaller hexagonal prism are one half that of the larger.

Similar Hexagonal Prisms

Illustration of 2 similar right hexagonal prisms. The height of the prism and length of the side of…

Illustration of a right decagonal pyramid. The base is a decagon and the faces are isosceles triangles. The hidden edges are shown in this illustration.

Decagonal Pyramid

Illustration of a right decagonal pyramid. The base is a decagon and the faces are isosceles triangles.…

Illustration showing a ditetragonal pyramid.

Ditetragonal Pyramid

Illustration showing a ditetragonal pyramid.

The frustum of a pyramid is the portion of a pyramid included between the base and a section parallel to the base.

Frustum Pyramid

The frustum of a pyramid is the portion of a pyramid included between the base and a section parallel…

The volume of the frustum of any pyramid is equal to the sum of the volumes of three pyramids whose common altitude is the altitude of the frustum, and whose bases are the lower base, the upper base, and the mean proportional between the bases of the frustum.

Frustum Pyramid for Volume

The volume of the frustum of any pyramid is equal to the sum of the volumes of three pyramids whose…

Illustration of a regular pyramid with a pentagon for a base.

Frustum of a Regular Pyramid With Pentagonal Base

Illustration of a regular pyramid with a pentagon for a base.

The frustum of a pentagonal pyramid is the portion of a pyramid included between the base and a section parallel to the base.

Frustum of Pentagonal Pyramid

The frustum of a pentagonal pyramid is the portion of a pyramid included between the base and a section…

Illustration of a right hexagonal pyramid with hidden edges shown. The base is a hexagon and the faces are isosceles triangles.

Hexagonal Pyramid

Illustration of a right hexagonal pyramid with hidden edges shown. The base is a hexagon and the faces…

Illustration of a right hexagonal pyramid with hidden edges shown. The base is a hexagon and the faces are isosceles triangles.

Hexagonal Pyramid

Illustration of a right hexagonal pyramid with hidden edges shown. The base is a hexagon and the faces…

Illustration of a hollow right decagonal pyramid. The base is a decagon and the faces are isosceles triangles. The pyramid is inverted, meaning that the vertex is at the bottom and the base is on top.

Inverted Decagonal Pyramid

Illustration of a hollow right decagonal pyramid. The base is a decagon and the faces are isosceles…

Illustration of a hollow right hexagonal pyramid. The base is a hexagon and the faces are isosceles triangles. The pyramid is inverted, meaning that the vertex is at the bottom and the base is on top.

Inverted Hexagonal Pyramid

Illustration of a hollow right hexagonal pyramid. The base is a hexagon and the faces are isosceles…

Illustration of a hollow right nonagonal pyramid. The base is a nonagon and the faces are isosceles triangles. The pyramid is inverted, meaning that the vertex is at the bottom and the base is on top.

Inverted Nonagonal Pyramid

Illustration of a hollow right nonagonal pyramid. The base is a nonagon and the faces are isosceles…

Illustration of a hollow right octagonal pyramid. The base is an octagon and the faces are isosceles triangles. The pyramid is inverted, meaning that the vertex is at the bottom and the base is on top.

Inverted Octagonal Pyramid

Illustration of a hollow right octagonal pyramid. The base is an octagon and the faces are isosceles…

Illustration of a hollow right rectangular pyramid. The base is a rectangle and the faces are isosceles triangles. The pyramid is inverted, meaning that the vertex is at the bottom and the base is on top.

Inverted Rectangular Pyramid

Illustration of a hollow right rectangular pyramid. The base is a rectangle and the faces are isosceles…

Illustration of a hollow right heptagonal (septagonal) pyramid. The base is a heptagon and the faces are isosceles triangles. The pyramid is inverted, meaning that the vertex is at the bottom and the base is on top.

Inverted Septagonal/Heptagonal Pyramid

Illustration of a hollow right heptagonal (septagonal) pyramid. The base is a heptagon and the faces…

Illustration of a hollow right heptagonal (septagonal) pyramid. The base is a heptagon and the faces are isosceles triangles. The pyramid is inverted, meaning that the vertex is at the bottom and the base is on top. The hidden edges are shown in this drawing.

Inverted Septagonal/Heptagonal Pyramid

Illustration of a hollow right heptagonal (septagonal) pyramid. The base is a heptagon and the faces…

Illustration of a right nonagonal pyramid with hidden edges shown. The base is a nonagon and the faces are isosceles triangles.

Nonagonal Pyramid

Illustration of a right nonagonal pyramid with hidden edges shown. The base is a nonagon and the faces…

Illustration of a right octagonal pyramid with hidden edges shown. The base is an octagon and the faces are isosceles triangles.

Octagonal Pyramid

Illustration of a right octagonal pyramid with hidden edges shown. The base is an octagon and the faces…

Illustration of a right pentagonal pyramid with hidden edges shown. The base is an pentagon and the faces are isosceles triangles.

Pentagonal Pyramid

Illustration of a right pentagonal pyramid with hidden edges shown. The base is an pentagon and the…

Illustration of a right pentagonal pyramid with hidden edges shown. The base is an pentagon and the faces are isosceles triangles.

Pentagonal Pyramid

Illustration of a right pentagonal pyramid with hidden edges shown. The base is an pentagon and the…

Illustration of a right pentagonal pyramid viewed from below with hidden edges shown. The base is an pentagon and the faces are isosceles triangles.

Pentagonal Pyramid

Illustration of a right pentagonal pyramid viewed from below with hidden edges shown. The base is an…

Illustration of a right pentagonal pyramid viewed from below. The base is an pentagon and the faces are isosceles triangles.

Pentagonal Pyramid

Illustration of a right pentagonal pyramid viewed from below. The base is an pentagon and the faces…

Illustration of pentagonal pyramid used to show that the volume is equal to one third of the product of its base by its altitude.

Pentagonal Pyramid For Volume

Illustration of pentagonal pyramid used to show that the volume is equal to one third of the product…

Illustration of a right rectangular pyramid with hidden edges shown. The base is a rectangle and the faces are isosceles triangles.

Rectangular Pyramid

Illustration of a right rectangular pyramid with hidden edges shown. The base is a rectangle and the…

Illustration of a right rectangular pyramid with hidden edges shown. The base is a rectangle and the faces are isosceles triangles. The height of the pyramid is much larger then the length and width of the base.

Rectangular Pyramid

Illustration of a right rectangular pyramid with hidden edges shown. The base is a rectangle and the…

Illustration of a right rectangular pyramid with hidden edges shown. The base is a rectangle and the faces are isosceles triangles.

Rectangular Pyramid

Illustration of a right rectangular pyramid with hidden edges shown. The base is a rectangle and the…

Illustration of a right rectangular pyramid with hidden edges shown. The base is a rectangle and the faces are isosceles triangles.

Rectangular Pyramid

Illustration of a right rectangular pyramid with hidden edges shown. The base is a rectangle and the…

Illustration of a regular pyramid with a pentagon for a base.

Regular Pyramid With Pentagonal Base

Illustration of a regular pyramid with a pentagon for a base.

Illustration of a regular pyramid with a square for a base.

Regular Pyramid With Square Base

Illustration of a regular pyramid with a square for a base.

Illustration of a right septagonal/heptagonal pyramid with hidden edges shown. The base is a heptagon and the faces are isosceles triangles.

Septagonal/Heptagonal Pyramid

Illustration of a right septagonal/heptagonal pyramid with hidden edges shown. The base is a heptagon…

Illustration of a non-right, or skewed, hexagonal pyramid with hidden edges shown. The base is a hexagon and the faces are isosceles triangles.

Skewed Hexagonal Pyramid

Illustration of a non-right, or skewed, hexagonal pyramid with hidden edges shown. The base is a hexagon…

Illustration of a non-right, or skewed, rectangular pyramid with hidden edges shown. The base is a rectangle and the faces are isosceles triangles.

Skewed Rectangular Pyramid

Illustration of a non-right, or skewed, rectangular pyramid with hidden edges shown. The base is a rectangle…

Illustration of triangular pyramid used to show that the volume is the limit of the sum of the volumes of a series of inscribed, or circumscribed prisms of equal altitude, if the number of prisms is indefinitely increased.

Triangular Pyramid For Volume

Illustration of triangular pyramid used to show that the volume is the limit of the sum of the volumes…

Illustration of triangular pyramid used to show that the volume is equal to one third of the product of its base by its altitude.

Triangular Pyramid For Volume

Illustration of triangular pyramid used to show that the volume is equal to one third of the product…

Illustration of 2 pyramids.

Pyramids

Illustration of 2 pyramids.

Illustration of 2 right pentagonal pyramids with hidden edges shown. The pentagonal bases are congruent, but the height of the smaller pyramid is one half that of the larger.

2 Right Pentagonal Pyramids

Illustration of 2 right pentagonal pyramids with hidden edges shown. The pentagonal bases are congruent,…

Illustration of 2 right rectangular pyramids with hidden edges shown. The rectangular bases are congruent, but the height of the smaller pyramid is one half that of the larger.

2 Right Rectangular Pyramids

Illustration of 2 right rectangular pyramids with hidden edges shown. The rectangular bases are congruent,…

Two triangular pyramids having equivalent bases and equal altitudes are equivalent.

Equivalent Triangular Pyramids

Two triangular pyramids having equivalent bases and equal altitudes are equivalent.

Illustration of pentagonal and triangular pyramids cut by a plane parallel to the bases.

Pyramids With Pentagonal and Triangular Bases

Illustration of pentagonal and triangular pyramids cut by a plane parallel to the bases.

Illustration of 2 regular pyramids.

Regular Pyramids

Illustration of 2 regular pyramids.

Illustration showing two rhombic pyramids.

Rhombic Pyramids

Illustration showing two rhombic pyramids.

Illustration of 2 similar right pentagonal pyramids with hidden edges shown. The height of the pyramid and length of the side of the pentagon (base) on the smaller pentagonal pyramid are one half that of the larger.

Similar Pentagonal Pyramids

Illustration of 2 similar right pentagonal pyramids with hidden edges shown. The height of the pyramid…

Illustration showing that the volume of 2 triangular pyramids, having the same trihedral angle of the one equal to a trihedral angle of the other, are to each other as the products of the three edges of these trihedral angles.

Triangular Pyramids for Volume

Illustration showing that the volume of 2 triangular pyramids, having the same trihedral angle of the…

A rectangular prism with labeled sides: AAAA are the four vertical parallel corners. BBBB and CCCC are the horizontal parallel edges.

Rectangular Prism

A rectangular prism with labeled sides: AAAA are the four vertical parallel corners. BBBB and CCCC are…

Illustration of a right rectangular pyramid that has been cut by a plane parallel to the base. The lower part is known as the frustum.

Rectangular Pyramid Cut By Plane

Illustration of a right rectangular pyramid that has been cut by a plane parallel to the base. The lower…