Why is the formula of area of triangle half times base time height?

Answer 1

The formula for the area of a triangle, ( \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} ), arises from the relationship between triangles and rectangles. The height of a triangle, when drawn from the vertex perpendicular to the base, divides the triangle into two right triangles. Since the area of a rectangle is base times height, the area of the triangle is half of that rectangle, leading to the formula involving the factor of one-half.