Building polyhedrons

Philip, look. What geometric shape do you think it's going to be if I fold along the dotted lines? What - shape? Lots of rectangles in some weird pattern. Let’s check.

Here is the picture Kim showed Philip. There are 6 rectangles. Four rectangles above each other. They are called 1, 2, 5 and 6. To the left of two is three, and to the right of two is four.

Fold number one up along the dotted line. Then fold up the two rectangles next to two. Rectangles three and four. Now fold rectangles five and six. Now it’s starting to look like a box with four sides.

Fold the last rectangle, number six. It’s like a lid on the box. When we folded all the rectangles together, they became a cuboid. Here is another shape, a pyramid with four sides. What does it look like if we unfold it?

Let’s look from above. If we fold out one of the four side surfaces, it looks like a triangle. Then we fold the other three side surfaces in the same way. another one and the last side surface, all are triangles - except the one in the middle, the base surface - that’s a square. What used to be a pyramid now looks like this - like a star.

Can you fold a pyramid in some other way? Yes you can. Here we see another pyramid with four sides from above. We unfold sides four and three. Then we unfold side two which is connected to side five.

Then we get another result. So it is actually possible to unfold the pyramid in several different ways. These three-dimensional shapes we’ve been working on have surfaces with straight sides - polygons. If we fold these polygons together we get a polyhedron - a cuboid or a pyramid. Knowing how a three-dimensional shape unfolds helps us calculate the total area on all sides of the shape.

It helps us calculate the total surface area. Look here, Kim, I've flattened myself. Can you calculate my total surface area, please? Philip, you're a cartoon character on a screen. You are always flat, and two-dimensional.

But I can fold you - to a polyhedron!