Geometry 12.2 notes
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)
