Question

The area of a trapezoid is given by the formula A= h(a+b)/2. solve for the formula for b.

Answer 1

The formula is

`A=((a+b)\cdot h)/(2)`

To solve for b, first, we multiply the equation by 2

`\begin{gathered} 2A=2\cdot((a+b)\cdot h)/(2) \\ 2a=(a+b)\cdot h \end{gathered}`

Then, we divide the equation by h

`\begin{gathered} (2A)/(h)=((a+b)h)/(h) \\ (2A)/(h)=a+b \end{gathered}`

At last, we subtract a from each side

`(2A)/(h)-a=a-a+b`

Hence, the final expression is

`b=(2A)/(h)-a`