Question

The area of a trapezoid is given by the formula A = (a + b). Solve the formula for b.

Answer 1

Starting from the given formula:

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

Multiply both sides of the equation by 2:

`\begin{gathered} \Rightarrow2* A=2*(h)/(2)(a+b) \\ \Rightarrow2A=h(a+b) \end{gathered}`

Divide both sides by h:

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

Substract a from both sides of the equation:

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

Therefore:

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