We get a picture that looks like the following:
As you should recall from geometry, the formula for the area of a trapezoid is
(b 1 + b 2 )h(Note: b 1 and b 2 are the two bases of the trapezoid.) Notice that each of the shapes is a trapezoid on its
side, so the height of each trapezoid is the length of the interval , and the bases are the y-values that
correspond to each x-value. We found these earlier in the rectangle example; they are, in order: 3, , 6,
, and 11. We can find the area of each trapezoid and add them up.Recall that the actual value of the area is or 12.67; the Trapezoid Rule gives a pretty good
approximation.