What is the formula for the area of a triangle?

The formula for the area of a triangle is derived from understanding how triangle dimensions relate to those of other shapes, particularly rectangles. The correct formula, expressed as ( \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} ), shows that the area of a triangle is half the product of its base and height.

In a rectangle, the area is calculated by multiplying the length (base) by the width (height). A triangle can be thought of as being formed by halving a rectangle that shares the same base and height. Thus, since the triangle occupies half of the area that would be filled by a rectangle with the same base and height, the area formula includes the factor of ( \frac{1}{2} ).

This relationship emphasizes that to determine the area of a triangle, one must accurately measure both the base, which is the length of one side, and the height, which is the perpendicular distance from the base to the opposite vertex. It's important to use the correct multiplication factor to reflect the triangular shape's geometry in relation to the rectangle.

By contrast, the formula that simply multiplies base by height, or those that add or double the area without