Answer:
7.5cm²
Complete question:What is the surface area of the 8-sided figure?
Step-by-step explanation:
Consider the half of the 8-sided die i.e the pyramid ABCDE:
As the base is 6 of the perimeter, so each side of the base is 6/4=3/2
Now, the distance between the tallest points is 2 cm, so the height of Pyramid ABCDE is 1 cm.
Considering the right triangle EOM:
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
[tex]\sqrt{1+ ( \frac{3}{4} )^{2} }= \sqrt{1+ \frac{9}{16} }= \sqrt{ \frac{25}{16} }= \frac{5}{4} (cm)[/tex]
5. So side EBC has area
[tex]\frac{1}{2}BC*EM= \frac{1}{2}* \frac{3}{2}* \frac{5}{4}= \frac{15}{16}[/tex]
6. The total area is 8*Area(EBC)=[tex]8* \frac{15}{16}= \frac{15}{2}=7.5 ( cm^{2} )[/tex]
