41. Find the area of a triangle whose base is x + 2 inches and whose height is x - 2 inches

To find the area of a triangle, you can use the formula:

\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]

For this triangle, the base is \( x + 2 \) inches, and the height is \( x - 2 \) inches. Plugging these values into the formula:

\[
\text{Area} = \frac{1}{2} \times (x + 2) \times (x - 2)
\]

Next, recognize that \( (x + 2)(x - 2) \) is a difference of squares:

\[
(x + 2)(x - 2) = x^2 - 4
\]

So the area becomes:

\[
\text{Area} = \frac{1}{2} \times (x^2 - 4)
\]

\[
\text{Area} = \frac{1}{2}x^2 - 2 \text{ square inches}
\]

Thus, the area of the triangle is:

\[
\boxed{\frac{1}{2}x^2 - 2} \text{ square inches}
\]

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**Do you want more details or have any questions?**  

Here are 5 related questions:

1. What is the area of the triangle if \( x = 4 \) inches?
2. How does the area change if the base is doubled and the height remains the same?
3. What would the area be if both the base and height were increased by 3 inches?
4. How do you calculate the area of a triangle if given only the three side lengths?
5. What happens to the area of the triangle as \( x \) increases?

**Tip:** Always simplify algebraic expressions carefully, especially when dealing with squares and differences.

Learn how to find the area of a triangle with a given base of x + 2 inches and height of x - 2 inches. This problem involves applying the area formula for triangles and simplifying algebraic expressions. Suitable for high school students.

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