What is the formula for the area of a triangle?

The formula for the area of a triangle is derived from the concept of how triangles can be formed from rectangles. To understand why the formula is 1/2 times the base times the height, consider that the area of a rectangle is calculated by multiplying the base by the height. A triangle can be thought of as half of a rectangle that shares the same base and height.

When you take a rectangle and split it along the diagonal, you create two right triangles. Each triangle represents half of the area of the rectangle, which is why the area of a triangle is given by the formula: area = 1/2 × base × height. This relationship holds true for any triangle, whether it is oriented vertically or horizontally, as long as you measure from the base to the vertex opposite the base, which is defined as the height.

Therefore, using the correct formula allows for accurate calculations of the area of any triangle format, ensuring students and practitioners in geometry can confidently determine the area in various applications.