Space Figures & Cross-Sections

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 Sections Describe 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