An 8-sided die is formed when two square pyramids are attached by their bases. The perimeter of the base shape is 6 centimeters.
The distance between the tallest points of the two pyramids is 2 centimeters. What is the surface area of the 8-sided figure?
2 answers:
1. Check the picture attached. Consider the half of the 8-sided die, that is the pyramid ABCDE:
2. The perimeter of the base is 6, so each side of the base is 6/4=3/2
3. The distance between the tallest points is 2 cm, si the height of Pyramid ABCDE is 1 cm.
4. Consider the right triangle EOM in the figure:
EO=1, OM= 3/4 (it is half of AB=3/2) and EM is the hypothenuse, so by the pythagorean theorem length of EM is
(cm)
5. So side EBC has area
6. The total area is 8*Area(EBC)=
2. The perimeter of the base is 6, so each side of the base is 6/4=3/2
3. The distance between the tallest points is 2 cm, si the height of Pyramid ABCDE is 1 cm.
4. Consider the right triangle EOM in the figure:
EO=1, OM= 3/4 (it is half of AB=3/2) and EM is the hypothenuse, so by the pythagorean theorem length of EM is
5. So side EBC has area
6. The total area is 8*Area(EBC)=
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