Let APQRS be a pyramid, where the base PQRS is a square of side length 20. The total surface area of the pyramid (including the base) is 1200. Let W, X, Y, and Z be the midpoints of AP, AQ, AR, and AS, respectively. Find the total surface area of frustum PQRSWXYZ (including the bases).
I remember that someone else posted a problem like this but it turns out the guest said the answer was incorrect, and I can't find it again.
+118673 The two pyramids are similar to one another.
the lengths of the sides are in the ration 1:2
so the surface areas are in the ratio 1:4 (I squared them)
The surface area of the whole thing is 1200 if I subtract the area of the base it is
1200-400=800
so the surface area of the top bit is 200
and the surface area of the base of the top bit is 100
So i think the surface area of the frustum is (800-200)+400+100 = 1100
I have not put any huge amount of thought into this. So maybe it is not right.
I assume you can plug the answer in and tell me if it is correct?
drumroll please.
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YOU ARE CORRECT!
Thank you so much. 5 stars, 5 thumbs up
epic
thanks
+118673 Thanks,
I do hope you understand it and could repeat it under exam conditions.
+876 Melody is just... great. She's a pro mathematician, and I cannot express the gratitude. You are so helpful! :)
