FTCE General Knowledge Math Practice Test

What does the formula 1/2 h(a + b) calculate?

1. Area of a trapezoid

2. Area of a circle

3. Volume of a pyramid

4. Perimeter of a trapezoid

The correct answer is: Area of a trapezoid

The formula \( \frac{1}{2} h(a + b) \) calculates the area of a trapezoid. In this formula, \( h \) represents the height of the trapezoid, while \( a \) and \( b \) are the lengths of the two parallel sides. The concept here is that the area of a trapezoid can be thought of as the average length of the two bases (sides) multiplied by the height. By adding the bases \( a \) and \( b \), dividing by 2 effectively finds the average length, and then multiplying by the height gives the total area. Other options do not fit this formula. For example, the area of a circle is calculated using the formula \( \pi r^2 \), while the volume of a pyramid would involve the formula \( \frac{1}{3} \text{Base Area} \times \text{Height} \). The perimeter of a trapezoid involves summing the lengths of all four sides, which is not represented in this formula.