Certified Pennsylvania Evaluator Practice Exam

How is the area of a triangle calculated?

1. 1/2 base x height

2. base x height

3. base x height / 2

4. height x height / 2

The correct answer is: 1/2 base x height

The area of a triangle is calculated using the formula that involves multiplying the base by the height and then dividing the result by two. This reflects the fact that a triangle is essentially half of a rectangle or parallelogram that shares the same base and height. Therefore, the formula to find the area can be expressed as one-half of the product of the base and height. When using the formula, you identify one side of the triangle to serve as the base, while the height is the perpendicular distance from this base to the opposite vertex. Since the area of a rectangle (or parallelogram) is determined by multiplying the base by the height and triangles occupy half of that space, the area is calculated as 1/2 base x height. This encapsulates the fundamental geometric relationship that defines how the area of a triangle is derived from its base and height. Other options provided do not accurately reflect the correct method for calculating the area of a triangle and may mislead you on the necessary mathematical operations involved.