Question

Solve each equation or formula for the specified variable.

$A=\frac{1}{2}h\left(a+b\right)$, for b.

Short answer

The required answer is $\frac{2A-ha}{h}=b$.

Step-by-step solution

Step 1- Simplify the right side of the equation

Use distributive property $a\left(b+c\right)=ab+ac$on right side of the equation.

$A=\frac{1}{2}ah+\frac{1}{2}bh$

– Isolate the variable y

Perform subtraction of $\frac{1}{2}ah$on both the sides of the equation.

$\begin{array}{l}A-\frac{1}{2}ah=\frac{1}{2}ah+\frac{1}{2}bh-\frac{1}{2}ah\\ A-\frac{1}{2}ah=\frac{1}{2}bh\end{array}$

Perform division of$\frac{1}{2}h$ on both the sides of the equation.

$\begin{array}{c}\frac{A-\frac{1}{2}ah}{\frac{1}{2}h}=\frac{\frac{1}{2}bh}{\frac{1}{2}h}\\ \frac{2A-ha}{h}=b\end{array}$

Step 3- Make the conclusion

As the variable b is isolated so the value equivalent to it represents its value.