**Geometry 12.2 not**es

**Prism** - is a polyhedron with two congruent faces called bases that lie in parallel planes.

The other faces are called **lateral faces** - are parallelograms formed by connecting the corresponding vertices of the bases.

**The segment connecting these vertices are lateral edges**.

Example:

Right Rectangular Prism Oblique Triangular Prism

**Surface Area of a Right Prism**:

SA = 2 (Area of the Base) + (perimeter of the base) (height between the bases)

**SA = 2A + Ph**

**Right Prism -** height is the perpendicular distance between bases and each lateral edge is perpendicular to both bases.

Example:

Rectangular Prism with length = 16 cm, width = 4 cm, and height = 9 cm.

SA = 2 B + Ph

SA = 2 (16)(4) + (16 + 4 + 16 + 4)(9)

SA = 488 square cm.

Recall **the area of an equilateral triangle is **

**A = the square root of 3 times the side squared divided by 4**

**Cylinder** - is a solid with congruent circular bases that lie in parallel planes.

The **altitude or height of the cylinder** is the perpendicular distance between the bases.

Example:

Given a Cylinder with radius of 5 ft. and the height of 12 ft., what is the surface area? Use 3.14 for pi.

SA = 2 B + Ph

The base is a circle so Area of a circle is = pi (5)(5) = 78.5 square feet

The perimeter of a circle is the circumference so C = pi (10) = 31.4

SA = 2B + Ph

SA = 2(78.5) + (31.4)(12) = 157 + 376.8 = 533.8 square feet.

**The Surface Area of a cylinder is **

**2 (pi) (r^2) + 2( pi) (r)( h)**