3D Geometry

Unit Review Sheet

Facts and Definitions

Lesson 1: Three-Dimensional Solids

• A polyhedron is a 3D solid made of multiple polygonal sides. The plural form of polyhedron is polyhedra or polyhedrons.
• A polygon that makes up a part of a geometric solid is called a face.
• A line where two faces intersect (meet) is called an edge.
• A vertex is the point where the edges meet (plural: vertices).
• A regular polyhedron is a solid in which all the faces are identical regular polygons. These are also called platonic solids.
• The face that is perpendicular to the height of the solid is called the base.
• A prism is a solid that has two congruent, parallel bases that are connected by lateral (side) faces shaped like parallelograms. Prisms are named after the shapes of their bases.
• In a convex polyhedron, the number of faces plus the number of vertices minus the number of edges always equals 2. This is called "Euler's Formula" and can be written as F + V − E = 2.
• A pyramid is a solid that has one polygonal base and faces shaped like triangles. Pyramids are named after the shape of their base.
• A net is a 2D representation of a 3D figure. It shows the number and shapes of the faces that compose the solid figure.

Lesson 2: Surface Area

• Surface area is the sum of the areas of all the faces of a three-dimensional solid.
• Surface area measures the total amount of space taken up by the outside of a 3D solid.
• The formula for the surface area of a rectangular prism is SA = 2LW + 2LH + 2HW.
• The formula for the surface area of a cube is SA = 6s².

Lesson 3: Volume

• Volume is the measure of space inside a three-dimensional shape.
• The formula for the volume of a rectangular prism is V = l × w × h, or V = lwh.
• The formula for the volume of a cube is V = s³.
• The formula for the volume of any prism is V = B × h, in which B represents the area of the base and h represents the perpendicular length from the base.

Lesson 4: Slices and Cross Sections

• A cross section is a two-dimensional shape formed when a plane intersects a three-dimensional solid.
• The shape and size of a cross section is determined by where the plane intersects the solid.
• A parallel cross section is made when a plane intersects a solid parallel to the base of the solid.
• A perpendicular cross section is made when a plane intersects a solid perpendicular to the base of the solid.
• Cross sections are uniform if each cross section made in the same direction results in congruent shapes.

Lesson 5: Problem Solving With Solids

• Surface area measures the space taken up by the outside of a solid figure, while volume measures the space taken up by the inside of the solid figure.
• Geometric formulas can be used as algebraic equations in order to find missing dimensions.

Lesson 6: Unit 7 Test

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Final Project: Building With Solids

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