Area is the number of square units that cover a two-dimensional region without gaps or overlaps.

• The area of region A is 8 square units.
• The area of the shaded region of B is square unit.

Any side of a parallelogram or triangle can be chosen its base. The length of this side is also called the base.

A base is a specific face of a prism or pyramid.

A prism has 2 identical bases that are parallel. A pyramid has 1 base.

A prism or pyramid is named for the shape of its base.

The word compose means “put together.” To compose a shape, put figures together to make a new shape.

The word cubed means “to the third power.” This is because a cube with side length has a volume of , or .

The word decompose means “take apart.” To decompose a shape, take it apart to make more than one new shape.

In expressions like and , the numbers 3 and the 2 are called exponents. They tell how many times a number is used as a factor.

For example, = , and .

Each flat side of a polyhedron is called a face.

For example, a cube has 6 faces that are all squares.

The height is the shortest distance from the base of the shape to the opposite side (for a parallelogram) or to the opposite vertex (for a triangle).

The height can be shown in more than one place. It is always perpendicular to the chosen base.

A parallelogram is a type of quadrilateral that has 2 pairs of parallel sides.

Here are 2 examples of parallelograms.

A polyhedron is a closed, three-dimensional shape with flat sides. When there is more than one polyhedron, they are called polyhedra.

Here are some drawings of polyhedra.

A prism is a type of polyhedron with 2 bases that are identical and parallel. The bases are connected by parallelograms.

Here are some drawings of prisms.

A pyramid is a type of polyhedron that has 1 base. All the other faces are triangles that meet at a single vertex.

Here are some drawings of pyramids.

A quadrilateral is a type of polygon that has 4 sides.

• A rectangle is an example of a quadrilateral.
• A pentagon is not a quadrilateral, because it has 5 sides.

A region is the space inside of a shape.

• Examples of two-dimensional regions are the inside of a circle and the inside of a polygon.
• Examples of three-dimensional regions are the inside of a cube and the inside of a sphere.

The word squared means “to the second power.” This is because a square with side length has an area of , or .

The surface area of a polyhedron is the number of square units that covers all of its faces with no gaps or overlaps.

For example, the 6 faces of a cube each have an area of 9 cm². So, the surface area of the cube is , or 54 cm².

Volume is the number of cubic units that fill a three-dimensional region with no gaps or overlaps.

This rectangular prism has 3 layers that are each 20 units³. So, the volume of the prism is 60 units³.