Solve for c A=1/2h(c+d)

$A = \frac{1}{2} h (c + d)$

Step 1

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

$\frac{1}{2} \cdot (h (c + d)) = A$

Step 2

Multiply both sides of the equation by $2$ .

$2 (\frac{1}{2} \cdot (h (c + d))) = 2 A$

Step 3

Simplify the left side.

Simplify $2 (\frac{1}{2} \cdot (h (c + d)))$ .

Apply the distributive property.

$2 (\frac{1}{2} \cdot (h c + h d)) = 2 A$

Apply the distributive property.

$2 (\frac{1}{2} (h c) + \frac{1}{2} (h d)) = 2 A$

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

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

$2 (\frac{h}{2} c + \frac{1}{2} (h d)) = 2 A$

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

$2 (\frac{h c}{2} + \frac{1}{2} (h d)) = 2 A$

$2 (\frac{h c}{2} + \frac{1}{2} (h d)) = 2 A$

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

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

$2 (\frac{h c}{2} + \frac{h}{2} d) = 2 A$

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

$2 (\frac{h c}{2} + \frac{h d}{2}) = 2 A$

$2 (\frac{h c}{2} + \frac{h d}{2}) = 2 A$

Apply the distributive property.

$2 \frac{h c}{2} + 2 \frac{h d}{2} = 2 A$

Cancel the common factor of $2$ .

Cancel the common factor.

$2 \frac{h c}{2} + 2 \frac{h d}{2} = 2 A$

Rewrite the expression.

$h c + 2 \frac{h d}{2} = 2 A$

$h c + 2 \frac{h d}{2} = 2 A$

Cancel the common factor of $2$ .

Cancel the common factor.

$h c + 2 \frac{h d}{2} = 2 A$

Rewrite the expression.

$h c + h d = 2 A$

$h c + h d = 2 A$

$h c + h d = 2 A$

$h c + h d = 2 A$

Step 4

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

$h c = 2 A - h d$

Step 5

Divide each term in $h c = 2 A - h d$ by $h$ and simplify.

Divide each term in $h c = 2 A - h d$ by $h$ .

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

Simplify the left side.

Cancel the common factor of $h$ .

Cancel the common factor.

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

Divide $c$ by $1$ .

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

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

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

Simplify the right side.

Simplify each term.

Cancel the common factor of $h$ .

Cancel the common factor.

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

Divide $- 1 d$ by $1$ .

$c = \frac{2 A}{h} - 1 d$

$c = \frac{2 A}{h} - 1 d$

Rewrite $- 1 d$ as $- d$ .

$c = \frac{2 A}{h} - d$

$c = \frac{2 A}{h} - d$

$c = \frac{2 A}{h} - d$

$c = \frac{2 A}{h} - d$

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