Hexagonal Prism

A hexagonal prism is a three-dimensional shape that has two hexagonal faces and six rectangular faces. The hexagonal faces are the bases of the prism, and the rectangular faces connect the corresponding sides of the two hexagons. The hexagonal prism gets its name from the fact that it has a hexagonal base.

Properties of a Hexagonal Prism:

It has 8 faces - 2 hexagonal faces and 6 rectangular faces.
It has 12 edges.
It has 6 vertices.
The opposite faces are parallel and congruent.
The lateral edges are all the same length.

Formulas for a Hexagonal Prism:

Surface Area (SA) = 2 * Base Area (B) + Perimeter of Base (P) * Height (h)

Volume (V) = Base Area (B) * Height (h)

Example Problem:

Find the surface area and volume of a hexagonal prism with a base edge length of 5 units and a height of 8 units.

Solution:
First, we need to calculate the base area (B) and the perimeter of the base (P): B = 3√3/2 * (5)^2 ≈ 64.95 square units P = 6 * 5 = 30 unitsNow, we can find the surface area and volume: SA = 2 * 64.95 + 30 * 8 = 129.9 + 240 = 369.9 square units V = 64.95 * 8 = 519.6 cubic units

Study Guide:

Understand the definition and properties of a hexagonal prism.
Learn the formulas for surface area and volume of a hexagonal prism.
Practice solving problems involving the surface area and volume of a hexagonal prism.
Identify real-life objects that have the shape of a hexagonal prism.
Review how to calculate the area of a hexagon and the perimeter of a hexagon, as these are used in the formulas for the hexagonal prism.

◂Math Worksheets and Study Guides Sixth Grade. Area

The resources above cover the following skills:

Geometry (NCTM)

Use visualization, spatial reasoning, and geometric modeling to solve problems.

Use geometric models to represent and explain numerical and algebraic relationships.

Measurement (NCTM)

Apply appropriate techniques, tools, and formulas to determine measurements.

Select and apply techniques and tools to accurately find length, area, volume, and angle measures to appropriate levels of precision.

Develop and use formulas to determine the circumference of circles and the area of triangles, parallelograms, trapezoids, and circles and develop strategies to find the area of more-complex shapes.

Connections to the Grade 6 Focal Points (NCTM)

Measurement and Geometry: Problems that involve areas and volumes, calling on students to find areas or volumes from lengths or to find lengths from volumes or areas and lengths, are especially appropriate. These problems extend the students' work in grade 5 on area and volume and provide a context for applying new work with equations.