Hexagonal Prism

A hexagonal prism is a three-dimensional shape with two hexagonal faces and six rectangular faces. The two hexagonal faces are the bases of the prism, while the six rectangular faces connect the corresponding sides of the two hexagons. The length of all the rectangular faces is the same, as is the length of the sides of the hexagons.

Properties of a Hexagonal Prism:

It has 8 faces in total: 2 hexagonal faces and 6 rectangular faces.
It has 12 edges.
It has 6 vertices.
The opposite faces are parallel and congruent.
The lateral faces (the 6 rectangular faces) are all rectangles.

Formulas for a Hexagonal Prism:

Let's denote the side length of the hexagon as s, the apothem (distance from the center of the hexagon to the midpoint of any side) as a, and the height of the prism as h. Then, the following formulas apply:

Surface Area (A) = 2 * (Area of hexagonal base) + (Perimeter of hexagon) * height

Volume (V) = (Area of hexagonal base) * height

Area of hexagonal base = 3/2 * s * a

Example Problem:

Find the surface area and volume of a hexagonal prism with side length s = 6 units, apothem a = 5 units, and height h = 10 units.

First, calculate the area of the hexagonal base using the formula: Area of hexagonal base = 3/2 * s * a = 3/2 * 6 * 5 = 45 square units.

Next, calculate the surface area: A = 2 * 45 + 6 * 6 * 10 = 90 + 360 = 450 square units.

Then, calculate the volume: V = 45 * 10 = 450 cubic units.

Now, you should have a good understanding of the properties, formulas, and calculations related to a hexagonal prism. Remember to practice solving problems to reinforce your understanding!

◂Math Worksheets and Study Guides Eighth Grade. Linear equations

The resources above cover the following skills:

Algebra (NCTM)

Represent and analyze mathematical situations and structures using algebraic symbols.

Explore relationships between symbolic expressions and graphs of lines, paying particular attention to the meaning of intercept and slope.

Grade 8 Curriculum Focal Points (NCTM)

Algebra: Analyzing and representing linear functions and solving linear equations and systems of linear equations

Students use linear functions, linear equations, and systems of linear equations to represent, analyze, and solve a variety of problems. They recognize a proportion (y/x = k, or y = kx) as a special case of a linear equation of the form y = mx + b, understanding that the constant of proportionality (k) is the slope and the resulting graph is a line through the origin. Students understand that the slope (m) of a line is a constant rate of change, so if the input, or x-coordinate, changes by a specific amount, a, the output, or y-coordinate, changes by the amount ma. Students translate among verbal, tabular, graphical, and algebraic representations of functions (recognizing that tabular and graphical representations are usually only partial representations), and they describe how such aspects of a function as slope and y-intercept appear in different representations. Students solve systems of two linear equations in two variables and relate the systems to pairs of lines that intersect, are parallel, or are the same line, in the plane. Students use linear equations, systems of linear equations, linear functions, and their understanding of the slope of a line to analyze situations and solve problems.

Connections to the Grade 8 Focal Points (NCTM)

Geometry: Given a line in a coordinate plane, students understand that all 'slope triangles' - triangles created by a vertical 'rise' line segment (showing the change in y), a horizontal 'run' line segment (showing the change in x), and a segment of the line itself - are similar. They also understand the relationship of these similar triangles to the constant slope of a line.