How is the area of a triangle calculated?

The area of a triangle is calculated by using the formula which involves the base and the height of the triangle. The correct formula states that the area is equal to one-half of the product of the base and the height. This formula can be derived by considering that a triangle can be seen as half of a rectangle or parallelogram formed by the base and the height.

To visualize this, if you take a rectangle with length equal to the base of the triangle and height equal to the height of the triangle, the area of the rectangle is simply base times height. Since a triangle is half of this rectangle, we take half of that area, leading to the formula of ( \frac{1}{2} \times \text{base} \times \text{height} ).

This understanding is crucial in geometry as it allows for the calculation of area for various applications in different fields, such as construction, architecture, and design. Numerical examples using this formula can help solidify the concept further, demonstrating its practical relevance.