A plane is drawn through the midpoint of a diagonal of a cube perpendicular to the diagonal. Determine the area of the figure resulting from the section of the cube cut by this plane if the edge of the cube is equal to a.


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Question Number 20194 by ajfour last updated on 23/Aug/17

$A p l a n e i s d r a w n t h r o u g h t h e$ $m i d p o i n t o f a d i a g o n a l o f a c u b e$ $p e r p e n d i c u l a r t o t h e d i a g o n a l .$ $D e t e r m i n e t h e a r e a o f t h e f i g u r e$ $r e s u l t i n g f r o m t h e s e c t i o n o f t h e$ $c u b e c u t b y t h i s p l a n e i f t h e e d g e$ $o f t h e c u b e i s e q u a l t o a .$
Commented by ajfour last updated on 24/Aug/17

$t h a n k y o u S i r .$
Commented by mrW1 last updated on 24/Aug/17

$the section is a regular hexagon with$ $side length b = \sqrt{2} (a / 2) = a / \sqrt{2}$ $A_{S} = \frac{3 \sqrt{3}}{2} b^{2} = \frac{3 \sqrt{3}}{2} \times \frac{a^{2}}{2} = \frac{3 \sqrt{3}}{4} a^{2}$
Commented by mrW1 last updated on 24/Aug/17

Commented by Einstein Newton last updated on 24/Aug/17

$Does it available on internet ?$
Commented by ajfour last updated on 24/Aug/17

$i d o n t k n o w, b u t l e s s c h a n c e .$
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