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.

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) (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

= = = = .

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 . = .
Hence, the lateral area of the pyramid is four times this value, i.e. = .
To get the total surface area of the pyramid, you need to add the area of the base square, which is = .

Answer. The lateral surface area of the pyramid is .
The total surface area of the pyramid is + = .

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