Question

Please please please help make sense of this

Answer 1

The enclosed shape is that of a trapezoid. The area of a trapezoid is the product of the height of it (measured perpendicular to the parallel bases) and the average length of the two parallel bases. The formula is generally written ...

... A = (1/2)(b₁ + b₂)·h

Here, the base lengths are the y-coordinates at x=4 and x=9. The height is the distance between those two x-coordinates: 9 - 4 = 5.

You are expected to find the y-values at those two points, then use the formula for the area of the trapezoid.

You can save a little work if you realize that the average of the two base lengths is the y-coordinate corresponding to the average x-coordinate: (9+4)/2 = 6.5. That is you only need to find the y-coordinate for x=6.5 and do the area math as though you had a rectangle of that height and width 5.

Going that route, we have

... y = 2(6.5) - 1 = 13 - 1 = 12

Then the trapezoid's area is

... A = 12·5 = 60 . . . . square units.