Question bank: Prisms and Pyramids: Layouts and Characteristics

Imagine you are an artist and want to create a very special gift box for your best friend. You decide that the paper box will be in the shape of a rectangular prism with dimensions of 4 cm in height, 6 cm in width, and 3 cm in depth. Before assembling it, you draw what we call the 'net' of the prism, which is how the box looks when we open and lay out all its faces. Now, think of a pyramid with a height of 5 cm and a base that is an equilateral triangle with sides of 6 cm. If you unfold the pyramid, you will have its net. Based on this, describe the nets of the rectangular prism and the pyramid with an equilateral triangle base and count the number of faces and edges of each. Remember to explain what edges and faces are.

Let's build a cardboard house for our school project model. To create the house, we need to decide which shape we will learn to make: a prism or a pyramid. Based on what you have learned about prisms and pyramids, describe which of these two geometric figures you would choose for the house and explain why you think this shape is the most suitable. Remember to think about the characteristics of each one, such as the shape of the faces and the number of edges. In your text, also explain how you think the house will look after it is assembled, considering the parts you will glue and the visual it will have.

Anna was given a school project that involves creating 3D models of different buildings in her city. She researched the structures and found that most buildings can be represented as either prisms or pyramids. Anna decided to start with a model of the city's central library, which she identified as a rectangular prism. To accurately create the model, she needs to cut out a net of the rectangular prism from a cardboard sheet. The net of a 3D shape is a 2D representation of the shape's faces that can be folded to form the shape. Help Anna identify the net of the rectangular prism so she can make sure she includes all the necessary faces and edges in her cardboard model. Which of the following is the correct net for a rectangular prism, and what are the characteristics of the net that distinguish it from the nets of other shapes she may encounter during her project?

In the Math class, teacher João presented to the students several flat and spatial geometric figures, highlighting the importance of recognizing the plane and spatial representations of prisms and pyramids and identifying their characteristics. He showed the planification of a triangular prism with 5 rectangular faces and 6 vertices, and asked the students to identify the number of edges and the shape of the base. Based on the provided planification, how many edges does the prism have and what is the shape of its base?

Imagine you are an architect and have been hired to build a building in the shape of a prism and a park in the shape of a pyramid. Draw the plans of these two structures and identify how many faces and edges each one will have. Remember to consider all the characteristics of a prism and a pyramid when making your drawings.