Surface area

Question

A rectangular prism column extends from the ground to the roof of a house.The base of the prism has a width of 4 in.The sides of the prism has a height of 21in.What is the surface area of the column in square inches?Include the base that meet the roof and ground.

Answer 1

A_rec = lw

A_sqr = w²

 

What we have here are 4 rectangles and 2 squares We know the bases are squares because each rectangular side of the prism has an edge of 4 inches long:

 

\----------\

 |           | \

 |           |  \   21in

 |           |   \

\----------\    \

 \             \    |

  \             \   |  4in

   \             \  |

    \---------- \|

            4in

 

(I hope that's coming in even in the final post for a good visualization)

21 in * 4 in = 84 in²

44 in² * 4 = 336 in²

(since we have 4 rectangles here)

 

4 in * 4 in = 16 in²

16 in² * 2 = 32 in²

(since we have 2 squares)

 

32 in² + 336 in² = 368 in²

So our final surface area--including the two bases--is 368 in²