A triangular pyramid and its net are shown. Rain uses the calculations below to conclude that the surface area of the triangular pyramid is 238.5 square inches. 3 (x 10 x 13) + (x 10 x 8.7) 3 (65) + 43.5 238.5 Is Rain correct? Use the drop-down menus to explain your reasoning. 12 in. 12 in. 13 in. 13 in. 8.7 in. E 12 in. 10 in. 10 in. 10 in

dude   i don't even know. i've been trying for hours.

step-by-step explanation:

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.

except if the answer is in the value of money, then, it will matter. it will have to be $0.40, but i can tell this is not a money question, so .4 should be the right one.