CK12 - Geometry

The surfaceareaof the rectangularsidesof the figureis calledthelateralareaof the figure.To find the
lateralarea,you couldadd up all of the areasof the rectangles.

Noticethat is the perimeterof the base.So anotherway to find the lateralarea of the figureis to multiply

the perimeterof the baseby , the heightof the figure.

Substituting , the perimeter, for , we get the formulafor any lateralarea of a right prism:

Now we can use the formulato calculatethe total surfacearea of the prism.Using for the perimeterand

for the area of a base:

Total surface= lateralarea + area of 2 bases

area

= (perimeterof base• height)+ 2 (areaof base)

=Ph+ 2B

To find the surfacearea of the figureabove,first find the area of the bases.The regularhexagonis made
of six congruentsmalltriangles.The altitudeof eachtriangleis theapothemof the polygon.Note:be
carefulhere—weare talkingaboutthe altitudeof the triangles,not the heightof the prism.We find the length

of the altitudeof the triangleusingthe PythagoreanTheorem,