A rectangular prism is completely packed with 63 cubes of edge length fraction 1 over 3 inch, without any gap or overlap. Which of these best describes the volume of this rectangular prism? 2 unit cubes and 2 smaller cubes of volume fraction 1 over 27 cubic inch each
2 unit cubes and 9 smaller cubes of volume fraction 1 over 27 cubic inch each
4 unit cubes and 2 smaller cubes of volume fraction 1 over 27 cubic inch each
4 unit cubes and 3 smaller cubes of volume fraction 1 over 27 cubic inch each

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.

oof

step-by-step explanation:

step-by-step explanation:

the answer is 89 d

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