What formula represents the area of a trapezoid?

The area of a trapezoid is calculated using the specific formula that involves the height and the lengths of the two parallel sides, often referred to as the bases. The correct formula states that the area is equal to one-half the height multiplied by the sum of the lengths of the parallel sides. This reflects how the area calculation takes into account both the height of the trapezoid and the average length of the bases, since the bases are parallel and the height is the perpendicular distance between them.

This formula, often expressed as Area = ½ × height × (base 1 + base 2), emphasizes that the area is influenced by both the height of the trapezoid and the dimensions of the bases. By using one-half of this sum, it ensures that you are effectively calculating the "average" width of the trapezoid when multiplied by the height, providing a correct measure of area.

Understanding this relationship is essential in geometry as it allows for accurate area calculations for trapezoidal shapes, which are common in various applications, from architecture to design.