Polyhedra

Warmup

Match each figure below with its description. Drag its name onto the line.

Activity #1

Investigate the Features of a Cube.

A cube, sometimes known as a hexahedron, is the solid figure bounded by six identical square faces that meet at right angles. It has eight vertices and
12 edges. This activity is all about making the investigation of these features. Follow the instructions below.

• Check the “Vertices” box and note how many vertices a cube has. You may want to spin the cube to see all around it.
• Check the “Edges” box and also note how many edges a cube has. Spin it around if need be.
• Check the “Faces” box to see how many faces. You can use the slider at the bottom for assistance.

• Answer the questions below.

Activity #2

Discover the Nets of a Square Pyramid.

The net of a rectangular pyramid consists of one rectangle and four triangles. The rectangle is the base of the pyramid, and the triangles are the lateral faces. Follow the instructions below to discover the net structure of a square pyramid.

• Move the horizontal slider back and forth to increase or decrease the base of the pyramid. ​
• Move the vertical slider up and down to increase or decrease the Altitude and slanting height of the pyramid. ​
• Click on the play button in the lower left corner to animate the faces of the pyramid.

• Answer the questions below.

Activity #3

Discover the Nets of a Cube. 

When the square faces of a cube are separated at the edges and laid out flat, they make a two dimensional figure called a net. In this activity, you are going to find that out.

• Pull the Net slider to the right to display the net of the cube. ​
• Check the Formula box to see the formula to find the Surface Area.

• Answer the questions below.

Activity #4

Create Your Own Polyhedron.

So far, you have discovered the net structure of a prism and a cube. We shall come back to this topic to explore the net structure of more shapes.

Before you start this exercise, click on the 3-dimensional plane(the plane not having the graph). Then click on to see the 3-D shapes that you can create with this applet. Now, follow the instructions below to create your own polygon.

• Click on the 2-D plane (the plane having the graph) to activate the tools. ​
• Click on the polygon tool, and create a polygon on the 2-D plane. Keep in mind that a Prism and a Pyramid can have any polygon as its base. So you can decide what type of polygon you want for the base of your figure. The polygon that you create, is also displayed on the 3-D plane. ​
• Click on the 3-D plane to activate the tools. ​
• Click on the tool icon and select the shape that you want. ​
• Click on the display in the 3-D plane. ​
• Enter the height without units of your shape. ​
• Click Ok. ​
• Click the Move tool . ​
• Play around with your shape. ​
• Click the Reset icon and keep practicing. It’s fun!

• Answer the questions below.

Challenge #1

Look at the prisms. What are their characteristics or features?

Challenge #2

Challenge #3