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

Answer:

7.5 sq centimeters

Step-by-step 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 $\sqrt{1+ ( \frac{3}{4} )^{2} }= \sqrt{1+ \frac{9}{16} }= \sqrt{ \frac{25}{16} }= \frac{5}{4}$ (cm)

5. So side EBC has area 
$\frac{1}{2}BC*EM= \frac{1}{2}* \frac{3}{2}* \frac{5}{4}= \frac{15}{16}$

6. The total area is 8*Area(EBC)=$8* \frac{15}{16}= \frac{15}{2}=7.5 ( cm^{2} )$