Big Ideas Math: Modeling Real Life, Grade 6
BI
Big Ideas Math: Modeling Real Life, Grade 6 View details
Chapter Review
Continue to next subchapter

Exercise 28 Page 336

A pyramid is a polyhedron in which one face (the base) can be any polygon and the other faces (the lateral faces) are triangles that meet at a common vertex called the vertex of the pyramid. The shape of the base tells the name of the pyramid.

Example Solid:

pentagonal prism
Practice makes perfect
A solid is a three-dimensional figure that encloses a space. A polyhedron is a solid whose faces are all polygons. Let's look at an example polyhedron.
polyhedron
A pyramid is a polyhedron that has one base. The lateral faces are triangles that meet in one common vertex. The shape of the base tells the name of the pyramid. In our case, we want to draw a square pyramid. We can tell by the name that the base is a square. Let's draw this pyramid!
pentagonal prism
Note that there are infinitely many possible square pyramids. This is just one.

Extra

For any polyhedron, the number of vertices V, faces F, and edges E satisfy the following formula. F+V=E+2 For example, in our square pyramid, we have 5 faces, 8 edges, and 5 vertices. Let's substitute these values for F, E, and V, and check that they satisfy the formula.
F+V=E+2
5+ 5? = 8+2
10=10 ✓
This formula was discovered by the Swiss mathematician Leonard Euler and it is called Euler's Formula. Euler is considered one of the greatest mathematicians of all time.