Question

What is the area of this shape

Answer 1

This is the area of a trapezoid and the formula for that is:
.5(h)(b1 + b2) where h is height and b1 and b2 are the base length or the length of the parallel sides.  therefore, our area is:
.5(16)(6+12)
8(18)
144
if you're wondering why the area formula works, construct another trapezoid but this time upside-down.  now flip it along it's height axis so you can align one of the side lengths of the 2 trapezoids and you have a parallelogram.
the base of this parallelogram is b1+b2 of the original trapezoid and the height still remains h so the area of this parallelogram is (h)(b1 + b2).  however, we want to find the area of the trapezoid but we find that the parallelogram is twice the area of our trapezoid so the area of the trapezoid is half the area of the parallelogram.  so area = .5(h)(b1 + b2).

let me know if you have any questions!