Could anyone help me with this question please?

construction = divide the figure into two parts.

now we have triangle abd and bdc.

first calculate the area of abd.

area of triangle= 1/2×base ×height

area of triangle= 1/2×18×7.5

area of triangle=67.5cm²

second calculate area of bdc

area of triangle=1/2×15.6×11.7

area of triangle=91.26cm²

area of the figure=area of abd + area of bdc

area of the figure=67.5cm²+ 91.26cm²

area of figure=158.76 cm².

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.