Find the area of a triangle if it's base is (3x-2y) and height is 4z.

The area \( A \) of a triangle can be found using the formula:

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

Given the base as \( (3x - 2y) \) and the height as \( 4z \), we substitute these values into the formula:

\[
A = \frac{1}{2} \times (3x - 2y) \times 4z
\]

Simplifying the expression:

\[
A = 2 \times (3x - 2y) \times z
\]

\[
A = 6xz - 4yz
\]

Thus, the area of the triangle is:

\[
A = 6xz - 4yz
\]

Would you like more details or have any questions?

Here are 5 related questions to expand this concept:
1. How would the area change if the base were doubled?
2. Can you find the perimeter of a triangle if given the lengths of all three sides?
3. How does changing the height to \( 5z \) affect the area?
4. What happens to the area if both base and height are tripled?
5. How would you calculate the area if the base were \( (x + y) \) instead?

**Tip:** Always remember that the area formula for triangles is applicable for any shape of triangle, whether it's right, scalene, or isosceles.

Find the area of a triangle if its base is (3x - 2y) and height is 4z.

Learn how to find the area of a triangle with a base of (3x - 2y) and a height of 4z. This algebraic problem uses the area of a triangle formula and provides a step-by-step solution. Suitable for students in Grades 7-10.

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