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-t

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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