Question

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Answer 1

1) h= side x (square root 3)/2
H=6 x (square root 3)/2
H=5.19 cm


2) H= 8x (square root 3)/2
H= 6.93 cm


3) Volume of the prism=
Area of the triangle x Length

Area= (Side^2 x square root 3)/4
As we have that the pen is touching the 3sides of the triangle, then
The pen is inscribed circle:
R= (side x square root 3)/6
6R=side x square root 3
Side= 6R/square root 3= 3.464 cm

Now put it in the formula
Area= (3.464^2 x square root 3)/4
Area of the triangle = 5.195

Now the volume of the prism
5.195 x 12= 41.569 cm