Conquer the College Math Placement Challenge 2025 – Step Up and Shine!

The formula for the area of a triangle is derived from the concept of how to calculate the area of a parallelogram. The area of a triangle is half that of a parallelogram because a triangle can be thought of as half of a parallelogram when drawn with the same base and height.

The formula \( A = \frac{1}{2} \times \text{base} \times \text{height} \) captures this relationship perfectly. Here, the "base" refers to the length of one side of the triangle, and the "height" is the perpendicular distance from that base to the opposite vertex.

This formula is universally applicable to all types of triangles, including scalene, isosceles, and equilateral triangles, as long as the base and height are properly identified. The factor of one-half is crucial because it accounts for the fact that we are only considering half of the area that would be occupied by a rectangle defined by the same base and height.

Other options do not accurately represent the area of a triangle. For example, adding the base and height gives no meaningful physical measurement of area, while multiplying the base and height together without the one-half factor will yield the area of a rectangle rather