Expert: Azeem Hussain - 5/16/2009

Question
the base of the right triangular prism is an equilateral triangle with a perimeter of 30 in. the base of right pentagonal prism is a regular pentagon of 30 in. both prisms are the same height but which one has greater lateral area. then i have to JUSTIFY MY REASONING. i know how to get all the sides of the bases and angles of the bases and i think the formula for LA is perimeter of the base times height.im not sure though. then i have to  figure out which one has the most surface area. i drew the figures but still need help. can you help me plz

Answer
Hey Matt,

Lateral area is the product of the base perimeter and the height.  Total surface area is lateral area plus the area of the two bases.  In this case, both prisms have equal base perimeters and heights, therefore they have equal lateral areas.  Because they have equal lateral areas, the only difference in their total surface areas comes down to their base areas.  Compare the base areas, that is triangle to pentagon, and the one with the larger base will have the greater total surface area.

Thanks for asking,
Azeem