Solid Geometry Surface Area Part 1 Polyhedrons 2

Solid Geometry (Surface Area)

Part 1. Polyhedrons 2. Nets of Polyhedrons 3. Surface Area of Polyhedrons 4. Surface Area Continued 5. Spring Break

Part 1

Vocabulary Area • ______ The amount of space in a two dimensional shape. Base. Any side of a parallelogram. • _______ Figures- A figure made up of two or more 2 -d figures. • Composite ________ Cube. A box-shaped solid object that has six identical square faces. • _______ Depth • _______ The horizontal distance from front to back. Edge • ______ A line segment joining two corners.

Vocabulary Face • ______ Any of the individual surfaces of a solid object. Height - The shortest distance from the base of a parallelogram to its • ______ opposite side. The vertical distance from top to bottom. Length - The distance from one side to another. • ____ Net - A two-dimensional pattern of a three-dimensional figure that can • _____ be folded/unfolded to show the form of the figure. Plane Shapes - Two dimensional figures. Flat Shapes • _______ • ______ Polyhedron - A three dimensional figure with flat polygonal faces, straight edges, and sharp corners or vertices. Prism - A prism is a polyhedron consisting of two parallel, congruent • _______ faces called bases.

Vocabulary • ____ Pyramid. Rectangle • _______ A pyramid is a polyhedron that has a base, which can be any polygon, and three or more triangular faces that meet at a point called the apex. A parallelogram having four right angles. Sphere - A geometrical figure that is perfectly round, 3 -dimensional and • ____ circular - like a ball. Square • _______ A rectangle having four right angles and four congruent sides. Surface Area - The total area of the surface of a three-dimensional object. • _______ Trapezoid • _____ A quadrilateral with one pair of parallel sides Triangle • _____ A figure with three sides and three angles.

Vocabulary Vertex - (plural: vertices) is a point where two or more straight lines meet. • _______ It is a Corner. - The amount of space inside a three dimensional shape. • Volume ____ Width • _______ The horizontal distance across a figure.

Today’s Standard 6. G. A. 4 Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.

Polyhedrons Essential Understandings: • Polyhedron is the name given to three dimensional polygons. • Poly means many and Hedron means face. So polyhedron translates to many faces. • There are two main types of polyhedrons: – Prisms: composed of 2 bases (any shape) and rectangular walls. – Pyramids: composed of one base (any shape) and triangular walls. • Polyhedrons are named for the shape of their bases, and this tells you how many walls they will have. • Examples:

Polyhedrons Essential Understandings: • Polyhedrons are named by the shape of their bases. • Types of Prisms: 1. 2. 3. 4. 5. 6. 7. Triangular Prism: 5 faces- 2 triangular bases and 3 rectangular walls Cube Prism: 6 faces- 6 square faces Square Prism: 6 faces- 2 square bases and 4 rectangular walls Rectangular Prism: 6 faces- 2 rectangular bases and 4 rectangular walls Pentagonal Prism: 7 faces- 2 pentagonal bases and 5 rectangular walls Hexagonal Prism: 8 faces- 2 hexagonal bases and 6 rectangular walls Etc… • Types of Pyramids: 1. 2. 3. 4. 5. Triangular Pyramid: 4 faces- 1 triangular base and 3 triangular walls Square Pyramid: 5 faces- 1 square base and 4 triangular walls Rectangular Pyramid: 5 faces- 1 rectangular base and 4 triangular walls Pentagonal Pyramid: 6 faces- 1 pentagonal base and 5 triangular walls Etc. .

Wrap it Up • Review • Questions • Exit Tickets

Part 2

Bell Work

Vocabulary Area • ______ The amount of space in a two dimensional shape. Base. Any side of a parallelogram. • _______ Figures- A figure made up of two or more 2 -d figures. • Composite ________ Cube. A box-shaped solid object that has six identical square faces. • _______ Depth • _______ The horizontal distance from front to back. Edge • ______ A line segment joining two corners.

Vocabulary Face • ______ Any of the individual surfaces of a solid object. Height - The shortest distance from the base of a parallelogram to its • ______ opposite side. The vertical distance from top to bottom. Length - The distance from one side to another. • ____ Net - A two-dimensional pattern of a three-dimensional figure that can • _____ be folded/unfolded to show the form of the figure. Plane Shapes - Two dimensional figures. Flat Shapes • _______ • ______ Polyhedron - A three dimensional figure with flat polygonal faces, straight edges, and sharp corners or vertices. Prism - A prism is a polyhedron consisting of two parallel, congruent • _______ faces called bases.

Vocabulary • ____ Pyramid. Rectangle • _______ A pyramid is a polyhedron that has a base, which can be any polygon, and three or more triangular faces that meet at a point called the apex. A parallelogram having four right angles. Sphere - A geometrical figure that is perfectly round, 3 -dimensional and • ____ circular - like a ball. Square • _______ A rectangle having four right angles and four congruent sides. Surface Area - The total area of the surface of a three-dimensional object. • _______ Trapezoid • _____ A quadrilateral with one pair of parallel sides Triangle • _____ A figure with three sides and three angles.

Vocabulary Vertex - (plural: vertices) is a point where two or more straight lines meet. • _______ It is a Corner. - The amount of space inside a three dimensional shape. • Volume ____ Width • _______ The horizontal distance across a figure.

Homework Check

Today’s Standard 6. G. A. 4 Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.

Polyhedrons Essential Understanding: A polyhedron is a three dimensional figure with flat polygonal faces, straight edges, and sharp corners or vertices. • In sixth grade we focus on two main types of polyhedrons – Prisms: A prism is a polyhedron, with two parallel faces called bases. The other faces are always parallelograms. The prism is named by the shape of its base http: //www. mathsisfun. com/geometry/prisms. html – Pyramids: A pyramid is a polyhedron that has a base, which can be any polygon, and three or more triangular faces that meet at a point called the apex. https: //www. mathsisfun. com/definitions/pyramid. html

Polyhedron Nets Essential Understanding: Nets are used to find the surface area of a three dimensional figures. • Nets are two dimensional layouts of three dimensional figures. In this unit we will focus on nets of prisms and pyramids. • Nets for three dimensional shapes can be classified by identifying the base(s) – A prism will have two congruent polygonal bases, and three or more parallelogram faces. Example: – A pyramid will have only one polygonal base and three or more triangular faces. Example: – The number of faces a solid has is determined by the number of edges the base has. Example:

Wrap it Up • Review • Questions • Exit Tickets

Part 3

Bell Work

Vocabulary Area • ______ The amount of space in a two dimensional shape. Base. Any side of a parallelogram. • _______ Figures- A figure made up of two or more 2 -d figures. • Composite ________ Cube. A box-shaped solid object that has six identical square faces. • _______ Depth • _______ The horizontal distance from front to back. Edge • ______ A line segment joining two corners.

Vocabulary Face • ______ Any of the individual surfaces of a solid object. Height - The shortest distance from the base of a parallelogram to its • ______ opposite side. The vertical distance from top to bottom. Length - The distance from one side to another. • ____ Net - A two-dimensional pattern of a three-dimensional figure that can • _____ be folded/unfolded to show the form of the figure. Plane Shapes - Two dimensional figures. Flat Shapes • _______ • ______ Polyhedron - A three dimensional figure with flat polygonal faces, straight edges, and sharp corners or vertices. Prism - A prism is a polyhedron consisting of two parallel, congruent • _______ faces called bases.

Vocabulary Pyramid • ____ Rectangle • _______ A pyramid is a polyhedron that has a base, which can be any polygon, and three or more triangular faces that meet at a point called the apex. A parallelogram having four right angles. Sphere - A geometrical figure that is perfectly round, 3 -dimensional and • ____ circular - like a ball. Square • _______ A rectangle having four right angles and four congruent sides. Surface Area - The total area of the surface of a three-dimensional object. • _______ Trapezoid • _____ A quadrilateral with one pair of parallel sides Triangle • _____ A figure with three sides and three angles.

Vocabulary Vertex - (plural: vertices) is a point where two or more straight lines meet. • _______ It is a Corner. - The amount of space inside a three dimensional shape. • Volume ____ Width • _______ The horizontal distance across a figure.

Homework Check

Today’s Standard 6. G. A. 4 Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.

Surface Area of a Prism Essential Understanding: A prism will have two congruent polygonal bases and three or more parallelogram faces. • To calculate the surface area of a prism, begin by creating a net to illustrate the figure two dimensional. Example: • Next, carefully label all of the given dimensions. Example: • Then, simply use the net to find area of each individual face/base. A table should be used to ensure precision. Example: • Finally, add the areas of all faces to determine the total surface area. Example: http: //www. virtualnerd. com/geometry/surface-area-volume-solid/prisms-cylindersarea/calculate-surface-area-rectangular-prism-net

Wrap it Up • Review • Questions • Exit Tickets

Part 4

Bell Work

Vocabulary Area • ______ The amount of space in a two dimensional shape. Base. Any side of a parallelogram. • _______ Figures- A figure made up of two or more 2 -d figures. • Composite ________ Cube. A box-shaped solid object that has six identical square faces. • _______ Depth • _______ The horizontal distance from front to back. Edge • ______ A line segment joining two corners.

Vocabulary Face • ______ Any of the individual surfaces of a solid object. Height - The shortest distance from the base of a parallelogram to its • ______ opposite side. The vertical distance from top to bottom. Length - The distance from one side to another. • ____ Net - A two-dimensional pattern of a three-dimensional figure that can • _____ be folded/unfolded to show the form of the figure. Plane Shapes - Two dimensional figures. Flat Shapes • _______ • ______ Polyhedron - A three dimensional figure with flat polygonal faces, straight edges, and sharp corners or vertices. Prism - A prism is a polyhedron consisting of two parallel, congruent • _______ faces called bases.

Vocabulary • ____ Pyramid. Rectangle • _______ A pyramid is a polyhedron that has a base, which can be any polygon, and three or more triangular faces that meet at a point called the apex. A parallelogram having four right angles. Sphere - A geometrical figure that is perfectly round, 3 -dimensional and • ____ circular - like a ball. Square • _______ A rectangle having four right angles and four congruent sides. Surface Area - The total area of the surface of a three-dimensional object. • _______ Trapezoid • _____ A quadrilateral with one pair of parallel sides Triangle • _____ A figure with three sides and three angles.

Vocabulary Vertex - (plural: vertices) is a point where two or more straight lines meet. • _______ It is a Corner. - The amount of space inside a three dimensional shape. • Volume ____ Width • _______ The horizontal distance across a figure.

Homework Check

Today’s Standard 6. G. A. 4 Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.

Surface Area of a Pyramid Essential Understanding: A pyramid will have only polygonal bases and three or more triangular faces. • To calculate the surface area of a pyramid, begin by creating a net to illustrate the figure two dimensional. Example: • Next, carefully label all of the given dimensions. Example: • Then, simply use the net to find area of each individual face/base. A table should be used to ensure precision. Example: • Finally, add the areas of all faces to determine the total surface area. Example:

Wrap it Up • Review • Questions • Exit Tickets

Part 5

Spring Break Begins Don’t Forget You Have Homework!!!

Vocabulary Area • ______ The amount of space in a two dimensional shape. Base. Any side of a parallelogram. • _______ Figures- A figure made up of two or more 2 -d figures. • Composite ________ Cube. A box-shaped solid object that has six identical square faces. • _______ Depth • _______ The horizontal distance from front to back. Edge • ______ A line segment joining two corners.

Vocabulary Face • ______ Any of the individual surfaces of a solid object. Height - The shortest distance from the base of a parallelogram to its • ______ opposite side. The vertical distance from top to bottom. Length - The distance from one side to another. • ____ Net - A two-dimensional pattern of a three-dimensional figure that can • _____ be folded/unfolded to show the form of the figure. Plane Shapes - Two dimensional figures. Flat Shapes • _______ • ______ Polyhedron - A three dimensional figure with flat polygonal faces, straight edges, and sharp corners or vertices. Prism - A prism is a polyhedron consisting of two parallel, congruent • _______ faces called bases.

Vocabulary Pyramid • ____ Rectangle • _______ A pyramid is a polyhedron that has a base, which can be any polygon, and three or more triangular faces that meet at a point called the apex. A parallelogram having four right angles. Sphere - A geometrical figure that is perfectly round, 3 -dimensional and • ____ circular - like a ball. Square • _______ A rectangle having four right angles and four congruent sides. Surface Area - The total area of the surface of a three-dimensional object. • _______ Trapezoid • _____ A quadrilateral with one pair of parallel sides Triangle • _____ A figure with three sides and three angles.

Vocabulary Vertex - (plural: vertices) is a point where two or more straight lines meet. • _______ It is a Corner. - The amount of space inside a three dimensional shape. • Volume ____ Width • _______ The horizontal distance across a figure.