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

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

Step 1

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

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

Step 2

Multiply both sides of the equation by $2$ .

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

Step 3

Simplify the left side.

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

Apply the distributive property.

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

Apply the distributive property.

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

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

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

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

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

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

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

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

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

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

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

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

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

Apply the distributive property.

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$B h + b h = 2 A$

$B h + b h = 2 A$

$B h + b h = 2 A$

$B h + b h = 2 A$

Step 4

Subtract $B h$ from both sides of the equation.

$b h = 2 A - B h$

Step 5

Divide each term in $b h = 2 A - B h$ by $h$ and simplify.

Divide each term in $b h = 2 A - B h$ by $h$ .

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

Simplify the left side.

Cancel the common factor of $h$ .

Cancel the common factor.

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

Divide $b$ by $1$ .

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

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

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

Simplify the right side.

Cancel the common factor of $h$ .

Cancel the common factor.

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

Divide $- B$ by $1$ .

$b = \frac{2 A}{h} - B$

$b = \frac{2 A}{h} - B$

$b = \frac{2 A}{h} - B$

$b = \frac{2 A}{h} - B$

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