A trapezoid has a height of 7 centimeters and an area of 32 square centimeters. If one base is increased by 5 centimeters and the height is doubled, what is the area of the new trapezoid, in square centimeters

Approximately 133.9 square cm (or 134 depending on rounding, see notes)

Step-by-step explanation:

Ok, If we slice one of the side triangles off a trapezoid, we really just have a rectangle. Using this knowledge makes it a little easier.

So, Imagine a rectangle now. You know height and you know area. The formula is A=B*H Where B is base, H is height and A is area. We can deconstruct this formula, and solve for the original base.

A=B*H

32=B*7 so B=32/7. B = 4.57142857 (Gross number, I know. We'll just keep it gross.)

Ok, So now we are increasing our base by 5 centimeters. I'm assuming by "one base" your teacher means that we are increasing both bases by 5, so essentially stretch out your shape. If it is in reality only one side, this gets quite a bit harder.

So, to get our new base, we take our gross number, 4.57142857 and add 5. This gives us 9.57142857. Height is doubled, so instead of the original height of 7, we have a height of 14. Now we can go back and use our old formula.

A=B*H

?=9.57142857*14

Area = 133.9, roughly. You can plug this into your calculator and it should spit out the decimals if you need it. Your teacher may also want you to just round up, so it may be 134 square cm