Question bank: Prisms and Pyramids: Layouts and Characteristics

João is playing with cardboard and decides to make some simple geometric constructions. He cuts some sheets into appropriate shapes and folds them to create three-dimensional figures. After creating a rectangular prism and a pyramid with the same base and height, he observes that the flat patterns of the figures have distinct characteristics. Considering the flat pattern of the prism and the flat pattern of the pyramid, describe the differences that João can observe regarding the number of edges and faces of each figure and explain how he can identify which is the flat pattern of which figure without folding them again. Tip: Remember that the flat pattern of a figure is the shape it would have if it were 'unfolded' in two dimensions, as if it were a template to be assembled later.

Imagine you are an architect and need to create special boxes to put small gifts in the shape of prisms and pyramids. To help, you decided to draw the flat pattern of some boxes. The flat pattern is a drawing that, when assembled, forms the box. Now, you have drawn the flat pattern of a prism-shaped box and a pyramid-shaped box. In the flat pattern, you can count how many faces (parts that form the box) and how many edges (lines where the faces meet) each box has. Describe the flat patterns you drew, stating how many faces and how many edges the prism flat pattern has and how many faces and how many edges the pyramid flat pattern has. Also, explain the difference between a prism and a pyramid.

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?

In math class, teacher Ana decided to create an activity for her students involving the recognition and counting of elements in three-dimensional geometric figures. She showed the students a pyramid with a triangular base. The pyramid was disassembled so that its faces were 'glued' onto a transparent paper, forming a flat drawing or plan. Considering that the original pyramid had 4 triangular faces and 1 quadrangular face (the base), the teacher asked the students to identify how many faces, edges, and vertices the flat drawing of the pyramid would have. How can you, as a student, determine the number of faces, edges, and vertices in the plan of the pyramid based on the information provided by teacher Ana?

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.