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Let APQRS be a pyramid, where the base PQRS is a square of side length 20. The total surface area of pyramid APQRS (including the base) is 1200. Let W, X, Y, and Z be the midpoints of $$\overline{AP}, \overline{AQ}, \overline{AR},$$ and $$\overline{AS},$$ respectively. Find the total surface area of frustum PQRSWXYZ (including the bases).

Jun 22, 2020

#1
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I believe that it doesn't make any difference if the pyramid is regular or not.

Total surface area = 1200.

Surface area of the base = 400.

Total surface area of the four sides is 1200 - 400  =  800.

1/2 of the area of each side is below the midline*; therefore 1/2·800  =  400 is below the midline.

Midline value of each side = 10   --->  area of the top base = 100.

Total surface area  =  400 + 400 + 100  =  900.

Jun 22, 2020
#3
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" 1/2 of the area of each side is below the midline "

The pyramid is cut horizontally, NOT vertically!!!

Guest Jun 23, 2020
#2
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Bottom square      Ab = 400

Top square            At = 100

Sides                     As = 600

Total area              A = 1100 units squared

Jun 23, 2020