FTCE General Knowledge Math Practice Test

Which formula gives the area of a parallelogram?

1. bh

2. 1/3Bh

3. 1/2 h(a + b)

4. sum of lengths of sides

The correct answer is: bh

The area of a parallelogram is calculated using the formula that involves the base and height, specifically the product of the base length and the corresponding height. The formula \( A = bh \) indicates that you take the length of the base (b) and multiply it by the height (h), which is the perpendicular distance from the base to the opposite side. This formula is derived from the concept that a parallelogram can be rearranged into a rectangle without changing its area; the base remains constant, and the height corresponds to that of the rectangle formed when the shapes are aligned. In contrast, the other formulas provided do not apply to the area of a parallelogram. For example, \( \frac{1}{3}Bh \) is used for calculating the volume of a pyramid, \( \frac{1}{2} h(a + b) \) is for the area of a trapezoid, and the sum of lengths of sides simply provides the perimeter, not the area. Thus, the correct choice accurately represents the fundamental relationship necessary to determine the area of a parallelogram.