## SAT SUBJECT TEST MATH LEVEL 1

## SOLID AND COORDINATE GEOMETRY

**CHAPTER 12 ****Solid Geometry**

**PRISMS**

Rectangular solids and cylinders are special cases of geometric solids called prisms. A ** prism** is a three-dimensional figure that has two congruent parallel

**. The (perpendicular) distance between the two bases is called the**

*bases***. Four prisms are depicted in the figure below.**

*height*On the Math 1 test, all of the prisms are ** right prisms**, which means that any line segment joining corresponding points on the bases is perpendicular to the bases. In the figure above, the first three prisms are right prisms; the fourth one is not. The volume formulas given in KEY FACTS K1 and K4 are special cases of the following formula.

**Key Fact K5**

**The formula for the volume of any right prism is V** =

*Bh*, where*B*is the area of one of the bases and*h*is the height.**EXAMPLE 4:** What is the volume of the triangular prism below?

First calculate the area of a base and multiply it by the height. By KEY FACT H11, the area of an equilateral triangle whose sides are 2 is . So the volume is .