The rectangular prism shown has a length of 5 cm, a height of 3 cm, and a width of 4 cm. what is the surface area of this prism?

94 cm2

Step-by-step explanation:

Hi, to answer this question we have to apply the next formula:

A = 2wl +2 lh+2hw

Where:

A = surface area of a prism

w = width

l= Length

h =height

Replacing with the values given and solving:

A = 2(4x5) +2 (5x3)+2(3x4)

A = 2(20) + 2(15)+ 2(12)

A= 40+30+24

A= 94 square centimeters

Feel free to ask for more if needed or if you did not understand something.

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.