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The equation provided is:

\[
A = \frac{1}{2} h (b + c)
\]

We need to solve for \( h \) in terms of \( A \), \( b \), and \( c \). Let's go step by step:

1. Start by multiplying both sides of the equation by 2 to eliminate the fraction:
   \[
   2A = h (b + c)
   \]

2. Now, divide both sides by \( (b + c) \) to solve for \( h \):
   \[
   h = \frac{2A}{b + c}
   \]

So, the solution for \( h \) is:

\[
h = \frac{2A}{b + c}
\]

Let me know if you need more details or further clarification!

Here are some related questions for you to consider:
1. How can this formula be used in real-world applications, such as calculating the height of a triangle?
2. What happens if \( b + c = 0 \)? Is there any restriction for the variables?
3. Can you rearrange this formula to solve for \( c \) instead?
4. How does this formula change if the \( \frac{1}{2} \) is replaced by a different constant?
5. What is the significance of the term \( b + c \) in this equation?

**Tip:** Always check if any variable in the denominator can make the expression undefined by becoming zero.

Solve for h in terms of A, b, and c. Given A = (1/2) * h * (b + c)

Learn how to solve for h in terms of A, b, and c. This algebra problem explains how to manipulate the equation A = (1/2) * h * (b + c) and isolate the variable h, with a step-by-step solution suitable for students in Grades 7-10.

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