Find the area of the shaded figure.

30

Step-by-step explanation:

lets see so step 1 would be to separate the shapes. to get a 3 by 6 rectangle and a triangle immediately you can figure out the area of the rectangle is 18, and from there you go to the triangle the triangle has a base measure of 6 and a height of 4 so you do 4x6 divided by 2 to get 12 so you add your two areas and you have a total area of 30

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.