Illustrative Math Alignment: Grade 7 Unit 7

This is part of a series of video animations of three-dimensional figures. These animations show different views of these figures: top, side, and bottom. Many of these figures are a standard part of the geometry curriculum and being able to recognize them is important.

Study these animations to learn the basic properties of these 3D figures. In particular, make a note of their sides, edges, and vertices. Look for any symmetries they have. Look for polygon shapes that are familiar. Finally, think of real-world examples that use these  figures.

Below we also include information about Platonic solids and 2D nets of these 3D figures. To get a better understanding of these 3D figures, study these basic forms.

This is part of a series of video animations of three-dimensional figures. These animations show different views of these figures: top, side, and bottom. Many of these figures are a standard part of the geometry curriculum and being able to recognize them is important.

Study these animations to learn the basic properties of these 3D figures. In particular, make a note of their sides, edges, and vertices. Look for any symmetries they have. Look for polygon shapes that are familiar. Finally, think of real-world examples that use these  figures.

Below we also include information about Platonic solids and 2D nets of these 3D figures. To get a better understanding of these 3D figures, study these basic forms.

This is part of a series of video animations of three-dimensional figures. These animations show different views of these figures: top, side, and bottom. Many of these figures are a standard part of the geometry curriculum and being able to recognize them is important.

Study these animations to learn the basic properties of these 3D figures. In particular, make a note of their sides, edges, and vertices. Look for any symmetries they have. Look for polygon shapes that are familiar. Finally, think of real-world examples that use these  figures.

Below we also include information about Platonic solids and 2D nets of these 3D figures. To get a better understanding of these 3D figures, study these basic forms.

Topic

3D Geometry

Description

This animated clip art image of an Antiprism illustrates its geometric properties by showing its two parallel, congruent polygonal faces connected by an alternating band of triangles. This animation helps visualize the symmetry and rotational aspects of the shape, making it an excellent tool for teaching concepts related to 3D geometry.

Animated math clip art like this antiprism is crucial for teaching as it enables students to see abstract concepts in motion, enhancing understanding and engagement. Teachers can use this image to demonstrate how antiprisms are constructed and explore their properties interactively.

Topic

3D Geometry

Description

This animation shows an antiprism with a horizontal cross-section, revealing its internal structure when sliced parallel to its bases. This visualization aids in understanding the spatial relationships and symmetry within the antiprism, making it a valuable teaching tool for discussing cross-sections and geometry.

Using animated math clip art like this helps students grasp complex spatial concepts by breaking them down into visual components. Teachers can use this image to explain how cross-sections can provide insight into the internal geometry of polyhedra.

Topic

3D Geometry

Description

This animation depicts an antiprism with a vertical cross-section, showing its internal structure when sliced perpendicular to its bases. This view is essential for understanding the vertical symmetry and arrangement of triangular faces, providing a deeper insight into the geometry of antiprisms.

Animated math clip art like this is important for teaching as it allows students to visualize and explore the internal structures of complex shapes dynamically. Teachers can use this image to discuss how vertical cross-sections reveal different aspects of a shape's geometry.

Topic

3D Geometry

Description

This animation shows the net of an antiprism unfolding and folding. A net is a 2D representation of a 3D shape that, when folded, creates the 3D object. For an antiprism, this includes two polygonal bases and a band of triangles.

Animated math clip art like this is invaluable for teaching as it helps students visualize the transition between 2D and 3D representations. Teachers can use this to explain concepts of surface area, shape properties, and spatial reasoning.

Topic

3D Geometry

Description

This animation shows the net of a rectangular prism folding into the rectangular prism. A rectangular prism's net consists of six rectangles: two identical pairs of congruent rectangles for the sides, and another pair for the top and bottom.

Animated math clip art like this is crucial for teaching as it helps students visualize how 2D shapes form 3D objects. Teachers can use this to explain concepts of surface area, volume, and the properties of prisms.

Topic

3D Geometry

Description

This animation shows the net of a triangular prism folding into the triangular prism. A triangular prism's net consists of two triangular bases and three rectangular faces that form the lateral surface.

Animated math clip art like this is crucial for teaching as it helps students visualize how 2D shapes form 3D objects. Teachers can use this to explain concepts of surface area, volume, and the properties of prisms.

Topic

3D Geometry

Description

This animation shows a rectangular prism, a three-dimensional figure with six rectangular faces. It's a fundamental shape in geometry, with applications in volume and surface area calculations.

Animated math clip art like this is essential for teaching as it allows students to visualize 3D shapes from different angles. Teachers can use this to explain concepts of volume, surface area, and properties of prisms.

Here's a potential script for teachers: "Observe this rectangular prism. Notice how it has six rectangular faces. How would you calculate its volume? Its surface area? How does this shape relate to real-world objects?"

Topic

3D Geometry

Description

This animation depicts a triangular prism, a three-dimensional shape with two triangular bases and three rectangular faces. It's an important shape in geometry with various real-world applications.

Using animated math clip art like this helps students visualize 3D shapes from different angles. Teachers can use this to explain concepts of volume, surface area, and properties of prisms.

Here's a potential script for teachers: "Observe this triangular prism. Can you identify its bases and lateral faces? How would you calculate its volume and surface area? Can you think of any objects in real life that have this shape?"

Topic

3D Geometry

Description

This animation shows a triangular prism with a horizontal cross-section. It illustrates that slicing the prism parallel to its base results in a rectangular cross-section that varies in size depending on the location of the slice.

Animated math clip art like this helps students understand the internal structure of prisms. Teachers can use this to discuss concepts such as congruence, cross-sectional area, and how this relates to the volume of a prism.

Topic

3D Geometry

Description

This animation depicts a triangular prism with a vertical cross-section. It shows how slicing the prism vertically results in a triangular cross-section, and all such triangles are congruent along the length of the prism.

Using animated math clip art like this provides students with a different perspective on the internal geometry of prisms. Teachers can use this to discuss concepts such as height, lateral area, and how vertical cross-sections relate to the surface area of a prism.

In this video students learn the basics of antiprisms, in the context of New York’s Freedom Tower, which has an antiprism design. They learn the properties of antiprisms, with the focus on those with a square base.

In this video students learn the basics of rectangular prisms, in the context of a New York residential tower: 432 Park Avenue. They learn the properties of rectangular prisms, with and without square bases, and the architectural requirements that influence the use of both types of rectangular prisms.

In this video students study a real-world application of triangular prisms: The Flat Iron Building in New York City. This building is an ideal example of a real-world prism and also provides a tie-in to right triangle geometry. This video describes the geometry of the Flat Iron Building, as well as its architecture. It includes animations that demonstrate the key features of triangular prisms.

In this video students learn the basics of prisms and anti prisms. They learn the properties of triangular prisms, rectangular prisms, triangular antiprisms, and rectangular antiprisms.

Topic

3D Geometry

Definition

An antiprism is a polyhedron composed of two parallel copies of an n-sided polygon, connected by an alternating band of triangles.

Description

Antiprisms are fascinating three-dimensional geometric figures that play a significant role in the study of polyhedra and spatial geometry. Unlike prisms, which have rectangular lateral faces, antiprisms feature triangular faces connecting their two parallel polygonal bases. This unique structure gives antiprisms distinct properties and applications in various fields of mathematics and engineering.

Topic

3D Geometry

Definition

A horizontal cross-section of a triangular prism is the shape obtained by cutting the prism with a plane parallel to its base.

Description

In three-dimensional geometry, a cross-section is the intersection of a plane with a solid figure. When this plane is parallel to the base of the solid, the resulting shape is called a horizontal cross-section. For a triangular prism with a rectangular base, this cross-section will always be a rectangle, similar in shape to the base of the prism.

Topic

3D Geometry

Definition

A net for a rectangular prism is a two-dimensional representation that, when folded, forms a three-dimensional rectangular prism.

Description

In the realm of three-dimensional geometry, the concept of a net is crucial for understanding how 3D shapes are constructed from 2D figures. A net for a rectangular prism is essentially a layout of all the faces of the prism in a single plane. This layout includes six rectangles that correspond to the six faces of the prism. By folding along the edges of these rectangles, one can recreate the three-dimensional shape of the rectangular prism.

Topic

3D Geometry

Definition

A net for a triangular prism is a two-dimensional figure that can be folded to form the surface of a three-dimensional triangular prism.

Description

In the context of three-dimensional geometry, a net is a crucial concept for understanding the surface area and structure of 3D shapes. Specifically, the net for a triangular prism consists of two triangular faces and three rectangular faces. When these faces are arranged in a specific two-dimensional pattern, they can be folded along the edges to form a triangular prism.

Topic

3D Geometry.

Definition

A net for an antiprism is a two-dimensional shape that can be folded to form a three-dimensional antiprism, which is a type of polyhedron with two parallel polygonal bases connected by an alternating band of triangles.

Description

In the realm of three-dimensional geometry, an antiprism is a fascinating polyhedron that extends the concept of prisms. Unlike regular prisms, which have two parallel bases connected by rectangular faces, antiprisms have two parallel bases connected by an alternating band of triangles. This unique structure results in a more complex and often more visually interesting shape.

Topic

3D Geometry

Definition

A prism is a three-dimensional solid object with two identical polygonal bases connected by parallelogram faces.

Description

In the realm of three-dimensional geometry, a prism is a polyhedron with two parallel, congruent bases connected by rectangular or parallelogram faces. The defining characteristic of a prism is that its cross-sections parallel to the bases are identical to the bases themselves. This property makes prisms a significant topic of study in geometry. 

Topic

3D Geometry

Definition

A rectangular prism is a three-dimensional figure with six rectangular faces, where opposite faces are congruent and parallel.

Description

The rectangular prism is a fundamental shape in three-dimensional geometry, serving as a building block for understanding more complex 3D structures. It is characterized by its three dimensions: length, width, and height, which are clearly labeled in the image. This shape is ubiquitous in both natural and man-made environments, making it a crucial concept for students to grasp.

Topic

3D Geometry

Definition

A triangular prism is a three-dimensional geometric solid with two congruent triangular bases and three rectangular faces.

Description

The triangular prism is a fundamental shape in three-dimensional geometry, playing a crucial role in understanding the properties of polyhedra and their applications in various fields. This prism is characterized by its unique structure, consisting of two parallel triangular bases connected by three rectangular faces. The shape of the triangular bases can vary, allowing for right, equilateral, isosceles, or scalene triangular prisms.

Topic

3D Geometry

Definition

A vertical cross section of a triangular prism is a two-dimensional shape obtained by slicing the prism parallel to its height, revealing a triangular face.

Topic

Geometry Basics

Definition

A polyhedron with two parallel faces and other faces that are triangular.

Description

An antiprism is a type of polyhedron that has two parallel faces connected by an alternating band of triangles. This geometric shape is significant in advanced geometry and has applications in fields such as crystallography and molecular chemistry. Understanding antiprisms helps in comprehending the properties of polyhedra and their role in three-dimensional space. For example, the volume of an antiprism can be calculated using specific geometric formulas, making it a useful concept in various scientific and mathematical applications.

Topic

Geometry Basics

Definition

A prism is a solid shape with two parallel, congruent bases connected by rectangular or parallelogram faces.

Description

Prisms are significant in the study of three-dimensional shapes. They have a uniform cross-section, allowing for easy calculations of volume and surface area. The volume can be calculated with the formula 

V = B⋅h

where B is the area of the base and h is the height. Prisms are commonly encountered in real-world applications such as packaging and structural designs, making them an essential concept in geometry.

The formula for the Surface Area of a Rectangular Prism.

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The formula for the Surface Area of a Triangular Prism.

Related Resources

To see resources related to this topic click on the Related Resources tab above.

The formula for the Volume of a Recantular Prism.

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To see resources related to this topic click on the Related Resources tab above.

Note: The download is a JPG file.

Related Resources

Topic

Geometric Models

Topic

Geometric Models

In this Google Earth Voyager story visit architectural landmarks in New York City to learn about the geometry of prisms. In this lesson, visit the Freedom Tower in Lower Manhattan and learn about antiprisms. Then build a scale model of the Freedom Tower.

Viewing Media4Math Stories on Google Earth

These Google Earth Voyager Stories are also available on Google Earth. Best viewed in Chrome, click on the links below to view these dynamic stories using Google's technology:

This collection of clip art images includes images of 3D figures and composite figures.

This collection of clip art images includes images of 3D figures and composite figures.

Topic

Geometry

Description

This math clip art image is part of a series showcasing 2D nets of 3D figures, specifically illustrating the net for a rectangular prism. The image displays a flattened representation of a rectangular prism, consisting of six connected rectangles arranged in a cross-like pattern. This visual aid is crucial for students to understand how a 3D rectangular prism can be unfolded into a 2D shape.

Topic

Geometry

Description

This math clip art image is part of a series illustrating 2D nets of 3D figures, with this particular image focusing on the net for a triangular prism. The image shows a flattened representation of a triangular prism, consisting of two triangular bases and three rectangular faces. This visual aid is essential for students to comprehend how a 3D triangular prism can be unfolded into a 2D pattern.

Topic

Geometry

Description

This math clip art image is part of a series showcasing 2D nets of 3D figures, specifically illustrating the net for an antiprism. The image displays a flattened representation of an antiprism, consisting of two polygonal bases (typically regular polygons) connected by a band of triangles. This visual aid is crucial for students to understand how a 3D antiprism can be unfolded into a 2D shape.

Topic

Volume

Description

A rectangular prism with dimensions labeled: length = 30, width = 10, and height = 8. The image shows how to find the volume of the prism using the formula for volume of a rectangular prism. This image illustrates Example 1: The caption explains how to calculate the volume of the rectangular prism using the formula V = l * w * h. The given dimensions are substituted into the formula: V = 30 * 10 * 8 = 2400..

Topic

Volume

Description

A green cylinder with a general radius y and height x. The radius is marked on the top surface, and the height is marked on the side. This image illustrates Example 10: The task is to find the volume of this cylinder. The volume formula V = πr2h is used, and substituting r = y and h = x, the volume is calculated as V = xy2π.

Topic

Volume

Description

A hollow green cylinder with an outer radius of 10 units, an inner radius of 9 units, and a height of 15 units. The radii are marked on the top surface, and the height is marked on the side. This image illustrates Example 11: The task is to find the volume of this hollow cylinder. The volume formula for a hollow cylinder V = πr12h1 - πr22h2 is used. Substituting values, the result is V = 285π.

Topic

Volume

Description

A hollow green cylinder with an outer radius y, an inner radius y - 1, and a height x. The radii are marked on the top surface, and the height is marked on the side. This image illustrates Example 12: The task is to find the volume of this hollow cylinder. Using V = π(r12h1 - r22h2), substituting values gives: V = πx(y2 - (y - 1)2= πx(2y - 1).

Topic

Volume

Description

A rectangular-based pyramid is shown with dimensions: base length 10, base width 8, and height 30. The image demonstrates how to calculate the volume of this pyramid. This image illustrates Example 13: The caption provides a step-by-step solution for calculating the volume of a pyramid with a rectangular base using the formula V = (1/3) * Area of Base * h. Substituting values: V = (1/3) * 8 * 10 * 30 = 800.

Topic

Volume

Description

A general rectangular-based pyramid is shown with variables x, y, and z representing the base dimensions and height. This example shows how to calculate the volume of a pyramid using variables instead of specific numbers. This image illustrates Example 14: The caption explains how to calculate the volume of a pyramid with a rectangular base using the formula V = (1/3) * Area of Base * h, which simplifies to V = (1/3) * x * y * z.

Topic

Volume

Topic

Volume

Description

A truncated rectangular-based pyramid is shown with variables x, y, and z representing dimensions. The smaller virtual pyramid has reduced dimensions by 3 units for both width and length and reduced height by z - 20. The image demonstrates how to calculate the volume in terms of variables. This image illustrates Example 16: The caption explains how to find the volume of a truncated pyramid using variables for both pyramids' dimensions. Formula: V = (1/3) * xy(z + 20) - (1/3) * (y - 3)(x - 3)(z), which simplifies to V = (1/3) * (xyz + 60x + 60y - 180).

Topic

Volume

Description

A green sphere with a radius labeled as 3. The image is part of a math example showing how to calculate the volume of a sphere. This image illustrates Example 17: The text describes finding the volume of a sphere. The formula used is V = (4/3) * π * r3, where r = 3. After substituting, the result is V = 36π.

Volume is a fundamental concept in geometry that helps students understand the space occupied by three-dimensional objects. In this collection, each example uses various geometric shapes to calculate volume, showcasing real-life applications of volume in different shapes.

Topic

Volume

Description

A green sphere with a radius labeled as x. This image is part of a math example showing how to calculate the volume of a sphere using an unknown radius. This image illustrates Example 18: The text explains how to find the volume of a sphere with an unknown radius x. The formula used is V = (4/3) * π * r3, and substituting r = x gives V = (4/3) * x3 * π.