Question

The height of a trapezoid is 8 inches and it’s area is 96 inches. One base of the trapezoids is 6 inches longer than the other base. What are the lengths of the bases? Explain how you found your answer

Answer 1

There is a common equation we use to find the Area of a trapezoid.
(a+b)h/2=A
Let's fill in what we know. We're not going to fill in any information about the bases.
(a+b)8/2=96
We can already tell that 8/2 will simplify to 4.
(a+b)4=96
Let's divide each side by 4.
a+b=24
Now, let's look at the information about the bases.
So, we will have this in terms of base a, since one base is longer than the other. This is how it'll look.
a +(a+6)=24
We can simplify that further.
2a+6=24
now subtract 6 from each side.
2a=18
Let's divide
9=a
So one side is 9, so the other one is 15. We should make sure everything makes sense by putting all the information in the formula to find area.
(9+15)8/2
24×4
96.
The lengths of the bases are 9 and 15 inches.