What is the formula for the area of a triangle?

The formula for the area of a triangle is indeed derived from the need to find the space enclosed within the triangle's three sides. To calculate the area, you take the base of the triangle and multiply it by the height, which is the perpendicular distance from the base to the opposite vertex. Since a triangle can be thought of as half of a rectangle that has the same base and height, the area of the triangle is then effectively half of that product. This is represented as:

Area = 1/2 × base × height.

This formula captures the essence of the triangle's geometry, emphasizing that the area is proportional to both the base and the height of the triangle. The other options pertain to different geometric shapes or concepts: the formula for the area of a rectangle, which is simply length times width, provides a different measurement of space; while the formula involving π relates to the area of a circle, demonstrating a completely different geometric figure. Thus, the correct formula for the area of a triangle is accurately captured in the answer given.