Olivia bought a large bead to hang from a necklace. The bead has five faces, nine edges, and six vertices. To which of the following types does the shape belong? And then we’re given five possible answers, sphere, cylinder, cube, triangular prism, or rectangular prism.
So this problem is asking us to identify a 3D shape, a bead that Olivia has bought to hang on a necklace. And we know that the bead is a 3D shape because it has faces, edges, and vertices. And these are all features of 3D shapes. And so the three clues that we can use to identify the shape are that it has five faces, nine edges, and six vertices. What do these three words mean? Let’s quickly remind ourselves.
A face of a 3D shape is a polygon or a 2D shape that makes up a flat surface of part of the shape. An edge of a 3D shape is a line segment where two faces meet together. And a vertex of a 3D shape is any point where several edges meet together. We can think of these as being like the corners of the shape, more than one vertex. We call it vertices.
So the question is asking us, which of these five shapes has five faces, nine edges, and six vertices? One way to find the answer could be to go through each shape separately and think about how many faces, edges, and vertices each shape has. But there is a quicker way. Two of the shapes on the list don’t have any vertices at all. So we don’t need to think about the other features. A sphere has no vertices. And a cylinder has no vertices. And so we can say that Olivia’s bead is not a sphere and is not a cylinder.
We’re now only left with three possible shapes, a cube, a triangular prism, and a rectangular prism. What do we know about cubes? We know that the faces on a cube are squares. But how many are there? If we look at our cube here, we can see that there are four faces around the side, one on the top, and one on the bottom. That’s six faces altogether. But Olivia’s bead has five faces. We don’t need to check the other features. We can say that her bead is not a cube.
What about a triangular prism? If we look at this triangular prism, we can see that it does have five faces, three rectangular faces around the sides and one triangular face on each end. That’s five altogether. Let’s check the other features to see if they match too. How many edges does a triangular prism have? On our diagram, we can see that there are two triangles, one at either end of the triangular prism. Each triangle has three sides. So that’s six edges. And then there are three long edges that connect them. That’s nine edges altogether.
How many vertices does a triangular prism have? The corners or the points of the shape are the same as the point of the triangles. And there are two triangles. So there are six vertices — five faces, nine edges, six vertices. It looks like the triangular prism is the correct answer. Let’s just check whether a rectangular prism has these features. Well, if we quickly count the faces of a rectangular prism, we can see that there are six rather like a cube. So we don’t need to check the other features. We know which of the five shapes Olivia’s bead is. Olivia’s bead must be a type of triangular prism because triangular prisms have five faces. They have nine edges and six vertices.