Question

The vertices of a trapezoid are points (0,x), (0,0), (y,0), and (z,x). Find the area in terms of x, y, and z.

I put 1/2x (y+z), I just want to make sure! thank you.

Answer 1

Your answer is correct. The two "bases" of the trapezoid are the line segments (0, 0)-to-(y, 0) and (0, x)-to(z, x), with lengths y and z, respectively. Then the average of the bases is
`\frac{y+z}2`. (We know they're the bases because the line segments are parallel.)

We multiply this by the height, which is given by the length of the line segment (0, 0)-to-(0,x), or x.

Hence the area is

`\frac{x(y+z)}2`

(which is identical to what you have).