The area of a trapezoid can be calculated using which formula?

• A. A = (b1 + b2) / 2 * h
• B. A = b * h
• C. A = (b1 + b2) * h
• D. A = π * r^2

Answer: (A)

The area of a trapezoid can be accurately calculated using the formula ( A = \frac{(b_1 + b_2)}{2} \times h ). In this formula, ( b_1 ) and ( b_2 ) represent the lengths of the two parallel sides (bases) of the trapezoid, and ( h ) is the height, which is the perpendicular distance between these two bases.

This formula essentially averages the lengths of the two parallel bases and then multiplies that average by the height to obtain the area. The reasoning behind this approach lies in the fact that the trapezoid can be viewed as a composite shape that can be broken down into simpler figures, such as rectangles or triangles, when determining its overall area.

The other formulas provided do not apply to trapezoids:

• The formula that suggests ( A = b \times h ) pertains to rectangles, where ( b ) is the length of one side and ( h ) is the height.

• Another option suggests ( A = (b_1 + b_2) \times h ) does not consider the division by 2, which is essential for averaging the two bases in a trapezo