Mathematics ACT Aspire Practice Test

How is the area of a triangle calculated?

1. Area = base * height

2. Area = base * height / 2

3. Area = (base1 + base2) * height

4. Area = height / 2

The correct answer is: Area = base * height / 2

The area of a triangle is calculated using the formula that involves the base and the height of the triangle. The correct formula states that the area is equal to the base multiplied by the height, divided by two. This stems from the fact that a triangle can be thought of as half of a parallelogram. When you multiply the base by the height, you effectively calculate the area of the rectangle that would be formed if you extended the triangle to form a parallelogram. However, since a triangle only occupies half of that space, dividing by two gives you the true area of just the triangle. This foundational concept in geometry is crucial for understanding how to measure the dimensions of triangular shapes. The other options do not accurately represent how to calculate the triangle's area. For instance, the first option suggests multiplying the base and the height without dividing by two, which would yield the area of a rectangle instead. The third option mistakenly adds two bases, which does not apply to a triangle, and the last option wrongly relates the height alone to the area, disregarding the base altogether. Thus, the formula that includes both the base and the height, while adjusting for the triangular shape, is essential for correctly determining the area of a triangle.