SOLUTION: Please help me solve this problem : A regular quadrilateral pyramid has a base side 16 cm and 6 cm height. Find the total area. Thank you.

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Question 966755: Please help me solve this problem :
A regular quadrilateral pyramid has a base side 16 cm and 6 cm height. Find the total area.
Thank you.
Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!

A sketch of your pyramid is schematically shown in the  Figure 1a  (not in the scale, though).
The base of the given pyramid is a square,  of course.

Draw the straight interval from the base center to the middle of the base side.
Its length is  16/2 = 8 cm.

Next,  draw the slant height from the vertex of the pyramid to that point  (Figure 1b).
Find the length of the slant height from the right triangle.  It is

h%5Bslant%5D = sqrt%286%5E2+%2B+8%5E2%29 = sqrt%2836+%2B+64%29 = sqrt%28100%29 = 10 cm.

Notice that the slant height has the same length for all lateral faces of the pyramid.                        



        Figure 1a        




        Figure 1b


Now,  the area of each triangular lateral face is  1%2F2.16%2A10 = 80 cm%5E2.
Hence,  the lateral area of the pyramid is four times this value,  i.e.  4%2A80 = 320 cm%5E2.
To get the total surface area of the pyramid,  you need to add the area of the base square,  which is  16%5E2 = 256 cm%5E2.

Answer.  The lateral surface area of the pyramid is  320 cm%5E2.
               The total surface area of the pyramid is  320 + 256 = 576 cm%5E2.