Solve A=1/2h(b+c)

$$A = 1 / 2 h ( b + c )$$

Solve for b

$$\left\{\begin{matrix}b=-c+\frac{2A}{h}\text{, }&h\neq 0\\b\in \mathrm{R}\text{, }&A=0\text{ and }h=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{2}h by b+c.

$$A=\frac{1}{2}hb+\frac{1}{2}hc$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{1}{2}hb+\frac{1}{2}hc=A$$

Subtract \frac{1}{2}hc from both sides.

$$\frac{1}{2}hb=A-\frac{1}{2}hc$$

The equation is in standard form.

$$\frac{h}{2}b=-\frac{ch}{2}+A$$

Divide both sides by \frac{1}{2}h.

$$\frac{2\times \frac{h}{2}b}{h}=\frac{2\left(-\frac{ch}{2}+A\right)}{h}$$

Dividing by \frac{1}{2}h undoes the multiplication by \frac{1}{2}h.

$$b=\frac{2\left(-\frac{ch}{2}+A\right)}{h}$$

Divide A-\frac{ch}{2} by \frac{1}{2}h.

$$b=-c+\frac{2A}{h}$$

Solve for A

$$A=\frac{h\left(b+c\right)}{2}$$