Space Figures & Cross-Sections

Section 11-1

Vocab• Polyhedron - 3-dimensional figure

whose surfaces are polygons• Face of polyhedron - each polygon

that forms the polyhedron• Edge - segment formed by the

intersection of two faces• Vertex - point where 3 or more

edges intersect • Cross-section – the intersection of

a solid & a plane.

Vocab Ctd.

Euler’s Formula

Group Activity

• Each group will construct several 3-dimensional figures from nets

• Groups will then record data and make conjectures on the relationship between faces, edges and vertices of a polyhedron

Use Euler’s Formula to find the number of edges on a solid with 6 faces and 8 vertices.

F + V = E + 2 Euler’s Formula

6 + 8 = E + 2 Substitute the number of faces and vertices.

12 = E Simplify.

A solid with 6 faces and 8 vertices has 12 edges.

You try

• Use Euler’s formula to find the number of edges on a polyhedron with eight triangular faces.

• 12 edges

Cross SectionsDescribe this cross section.

The plane is parallel to the triangular base of the figure, so the cross section is also a triangle.

You try

• Describe the cross-section.

Drawing Cross Sections

Draw and describe a cross section formed by a vertical plane intersecting the top and bottom faces of a cube.

If the vertical plane is parallel to opposite faces, the cross section is a square.

Sample: If the vertical plane is not parallel to opposite faces, the cross section is a rectangle.

You try

• Draw & describe the cross section formed by a horizontal plane intersecting the left and right faces of the cube.

Closure