Why is the formula for the area of a triangle expressed as ½bh?

The formula for the area of a triangle, expressed as ( \frac{1}{2}bh ), is derived from the relationship between triangles and parallelograms. A triangle can be thought of as half of a parallelogram. To see this clearly, if you take a parallelogram and draw a diagonal from one vertex to the opposite vertex, you create two congruent triangles.

The area of a parallelogram is calculated by multiplying the base by the height (( bh )). Since a triangle is essentially half of that parallelogram, its area is represented as half the area of the parallelogram, which is why we say the area of a triangle is ( \frac{1}{2}bh ). This fundamental relationship helps in understanding why the area calculation for triangles works as it does, reinforcing the concept of geometric shapes and their properties.

Other options do not accurately reflect the geometric principles involved. The statement regarding the base and height would misinterpret the basic definitions of triangle dimensions. The claim of applicability only to isosceles triangles neglects that the formula is valid for all types of triangles. Lastly, relating the area of a trapezoid to triangles does not directly connect to the derivation