body{margin:0;} noscript{z-index: 10000; position: fixed; display: block; height: 100%; width: 100%; background: #fff;} noscript .fa{font-size: 40px; display:block; color: #daa520;} noscript div{margin-top: 6%; padding-left: 20px; padding-right: 20px; text-align: center;} ! You must have JavaScript enabled to use this site.

Big Ideas Math: Modeling Real Life, Grade 6

BI

Big Ideas Math: Modeling Real Life, Grade 6 View details

Practice Test

Continue to next subchapter

Exercise 8 Page 338

A prism is a polyhedron that has two parallel, identical bases. The lateral faces are parallelograms. The shape of the base tells the name of the prism.

Example Solid:

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 prism is a polyhedron that has two parallel, identical bases. The lateral faces are parallelograms. The shape of the base tells the name of the prism. In our case, we want to draw an octagonal prism. We can tell by the name that the bases are octagons. Let's draw this prism!

pentagonal prism

Note that there are infinitely many possible octagonal prisms. 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 octagonal prism, we have 10 faces, 24 edges, and 16 vertices. Let's substitute these values for F, E, and V, and check that they satisfy the formula.

F+V=E+2

SubstituteValues

Substitute values

10+ 16? = 24+2

Add terms

26=26 ✓

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.

Subchapter links

Exercises