Solids: prisms, pyramids and their edges

This solid rests on a rectangular face. Its front and back faces are the same triangle. Hidden edges are shown as dotted lines. How many edges does it have? Try it first. Pause if you like. Look for the face at the other end. What stays the same when the solid turns? Watch the solid turn. There is a triangle at each end, the same shape and size. Dotted lines show edges hidden behind its faces. The front and back faces are the same triangle, the same shape and size, so the solid is a prism. Count round the front triangle. One. Two. Three. Edges round the triangular face at the front: three. Turn to the other end. This is the matching triangle at the back. The blue edges already counted stay blue. Count round this back triangle. One. Two. Three. Edges round the triangular face at the back: three. Now follow the edges joining the front to the back. Each front corner has one joining edge. Dotted edges belong to the solid too. One. Two. Three. Edges joining a corner at the front to the corner behind it: three. Number of edges equals three plus three plus three, which equals nine. The solid is a triangular prism. It has nine edges. We counted each triangular end, then the joining edges. Every edge belongs to just one of those groups.

One face of this solid is a rectangle and the other four faces are triangles. Hidden edges are shown as dotted lines. How many edges does it have? Try it first. Pause if you like. Does the far end have another matching face, or a point? Turn the solid and look at the top. Its triangular faces all meet at one point. The rectangular face stays at the bottom. Every face except the bottom one is a triangle. All four meet at the same point at the top, so the solid is a pyramid. It is not a prism. A prism has a second matching face at its far end, but this solid has a point there. Count round the rectangular base. One. Two. Three. Four. Edges round the rectangular face at the bottom: four. Next, count the edges from the base corners to the top point. Include the dotted edge behind the faces. One. Two. Three. Four. Edges running from the rectangle corners to the point at the top: four. Number of edges equals four plus four, which equals eight. The solid is a rectangular pyramid. It has eight edges. Name the solid from its faces. Count its edges in groups, including the hidden edges.