Question

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?

Answer 1

7.5 sq centimeters

Explanation:

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Answer 2

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
`\sqrt{1+ ( (3)/(4) )^(2) }= \sqrt{1+ (9)/(16) }= \sqrt{ (25)/(16) }= (5)/(4)` (cm)

5. So side EBC has area

`(1)/(2)BC*EM= (1)/(2)* (3)/(2)* (5)/(4)= (15)/(16)`

6. The total area is 8*Area(EBC)=
`8* (15)/(16)= (15)/(2)=7.5 ( cm^(2) )`