Solve for a a=1/2(a+b)h

$a = \frac{1}{2} (a + b) h$

Simplify $\frac{1}{2} \cdot ((a + b) h)$ .

Apply the distributive property.

$a = \frac{1}{2} \cdot (a h + b h)$

Apply the distributive property.

$a = \frac{1}{2} (a h) + \frac{1}{2} (b h)$

Multiply $\frac{1}{2} (a h)$ .

Combine $a$ and $\frac{1}{2}$ .

$a = \frac{a}{2} h + \frac{1}{2} (b h)$

Combine $\frac{a}{2}$ and $h$ .

$a = \frac{a h}{2} + \frac{1}{2} (b h)$

Multiply $\frac{1}{2} (b h)$ .

Combine $b$ and $\frac{1}{2}$ .

$a = \frac{a h}{2} + \frac{b}{2} h$

Combine $\frac{b}{2}$ and $h$ .

$a = \frac{a h}{2} + \frac{b h}{2}$

Subtract $\frac{a h}{2}$ from both sides of the equation.

$a - \frac{a h}{2} = \frac{b h}{2}$