Introduction and Background
Theory
A prism is a solid geometric figure with three-dimensional shape. It has two identical and equidistant polygonal faces that form the base, and its other faces are parallelograms that form the lateral surface, known as the prism. The calculation of the surface area of these figures is a fundamental concept of geometry that has practical applications in everyday life, such as architecture, design projects, space planning, and engineering.
To calculate the total area of a prism, we add the area of the bases to the lateral surface area. The lateral surface area is calculated by multiplying the perimeter of the base by the height. The total surface area includes the area of the bases, which must be multiplied by two (since we have two bases).
Context
Prisms are all around us. Think about a cardboard box, a rectangular prism; the building where you live, a cylinder which is a particular type of prism, and so on. Knowing the surface area of these figures is essential in many professions. Architects need to know the surface area of rooms to design functional spaces. Engineers need to calculate the surface area of materials to determine how much is needed for a project.
In terms of its importance in STEAM (Science, Technology, Engineering, Arts, and Mathematics) fields, calculating the surface area of prisms is a key skill for civil engineers, who design resistant and efficient structures, and for designers creating three-dimensional objects for production.
Hands-on Activity: "Building Prisms and Calculating Surface Area"
Project Goal
The goal of this project is to allow students to apply their knowledge of mathematics, geometry, and teamwork to build a three-dimensional prism using everyday materials and then calculate the prism's surface area.
Detailed Project Description
Students will work in groups of 3 to 5 students. Each group will choose a type of prism (triangular prism, rectangular prism, hexagonal prism, etc.) to build and calculate its surface area.
It is important for students to plan their prism by deciding ahead of time what the dimensions of each side will be. They should calculate the area of each face of their prism before they build it to check if their predictions match their results after they build it.
Materials
- Cardstock or thin cardboard
- Pencil, ruler, and eraser
- Scissors
- Tape or glue
- Calculator (optional)
Step-by-Step Guide
- Choose the type of prism you are going to build. Decide on the dimensions of the prism, meaning the length of each side, the height, etc.
- Draw the net of your prism on the cardstock or thin cardboard. Remember to include extra flaps on the edges to tape the faces together.
- Carefully cut out the prism net.
- Fold the cardboard along the lines of the drawing to form the prism.
- Use tape or glue to attach the flaps to form the prism.
- Calculate the area of each face of your prism and add these areas together to get the total surface area.
- Compare the result of your surface area calculation with your prediction before you built the prism.
Project Deliverables
Each group will turn in their completed prism and a written report that includes the following:
Introduction: Describe the type of prism chosen, its real-world applications, and the objective of the project.
Methods: Provide a detailed description of the prism construction process, including any calculations done to determine the dimensions and areas of the faces and any difficulties encountered. Present the theory behind the calculations performed.
Results: Discuss the accuracy of the surface area calculations, what the group learned from doing the project, and how the knowledge gained can be applied in real-world situations.
References: List any books, websites, and/or videos used to help complete the project.
The report should complement the hands-on component, allowing students to demonstrate both their practical application and theoretical understanding of prism surface area.
