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

Question

anonymous · Answer

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)