Question

A trapezoid has an area of 4 square units and a height of 1 unit what are the possible whole number lengths for the bases

Answer 1

Use the formula for the area of a trapezoid (A) with bases (b1 and b2) and height (h).

A=(1/2)(b1+b2)(h)

We know:
A=4, h=1.

Plug in those values.

4=1/2(b1+b2)(1)
4=(b1+b2)/2
8=b1+b2
b2=8-b1

Now, we can have these possible values for b1 and b2.

b1=1,
b2=8-1=7

b1=2,
b2=8-2=6

b1=3,
b2=8-3=5

b1=4,
b2=8-4=4<---This is eliminated because the bases cannot be equal. If they were equal, we would have a rectangle, not a trapezoid.

The rest are just the above with b1 and b2 switched. So it is unnecessary to go on.

Thus, in units, the possible whole number lengths for the bases are:

(1,7)
(2,6)
(3,5)