Hexahedron

A hexahedron is a geometric solid shape that has six faces, twelve edges, and eight vertices. It is a three-dimensional figure that is made up of six identical square faces. The hexahedron is also known as a cube, and it is a regular polyhedron, meaning all of its faces are congruent and all of its angles are right angles.

Properties of a Hexahedron:

It has 6 faces, all of which are squares
It has 12 edges
It has 8 vertices
All of its faces are congruent
All of its angles are right angles

Formulas and Calculations:

Surface Area of a Hexahedron: 6a² where a is the length of each side of the hexahedron.

Volume of a Hexahedron: a³ where a is the length of each side of the hexahedron.

Example Problem:

Find the surface area and volume of a hexahedron whose side length is 5 units.

Surface Area = 6 × 5² = 6 × 25 = 150 square units

Volume = 5³ = 125 cubic units

Study Guide:

When studying hexahedrons, it is important to understand the properties of the shape, the formulas for surface area and volume, and how to calculate these values. Practice identifying hexahedrons in everyday objects and understanding their properties.

Key points to remember:

A hexahedron has 6 faces, 12 edges, and 8 vertices
All faces are squares
All angles are right angles
Surface Area = 6a² and Volume = a³

◂Math Worksheets and Study Guides Seventh Grade. Algebraic Equations

The resources above cover the following skills:

Algebra (NCTM)

Use mathematical models to represent and understand quantitative relationships.

Model and solve contextualized problems using various representations, such as graphs, tables, and equations.

Grade 7 Curriculum Focal Points (NCTM)

Number and Operations and Algebra: Developing an understanding of operations on all rational numbers and solving linear equations

Students extend understandings of addition, subtraction, multiplication, and division, together with their properties, to all rational numbers, including negative integers. By applying properties of arithmetic and considering negative numbers in everyday contexts (e.g., situations of owing money or measuring elevations above and below sea level), students explain why the rules for adding, subtracting, multiplying, and dividing with negative numbers make sense. They use the arithmetic of rational numbers as they formulate and solve linear equations in one variable and use these equations to solve problems. Students make strategic choices of procedures to solve linear equations in one variable and implement them efficiently, understanding that when they use the properties of equality to express an equation in a new way, solutions that they obtain for the new equation also solve the original equation.