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

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

Rewrite the equation as $\frac{1}{2} \cdot ((a + b) h) = A$ .

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

Multiply both sides of the equation by $2$ .

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

Simplify the left side.

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

Apply the distributive property.

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

Apply the distributive property.

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

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

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

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

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

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

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

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

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

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

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

Apply the distributive property.

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$a h + b h = 2 A$

Factor $h$ out of $a h + b h$ .

Factor $h$ out of $a h$ .

$h a + b h = 2 A$

Factor $h$ out of $b h$ .

$h a + h b = 2 A$

Factor $h$ out of $h a + h b$ .

$h (a + b) = 2 A$

Divide each term in $h (a + b) = 2 A$ by $a + b$ and simplify.

Divide each term in $h (a + b) = 2 A$ by $a + b$ .

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

Simplify the left side.

Cancel the common factor of $a + b$ .

Cancel the common factor.

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

Divide $h$ by $1$ .

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

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

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