How is the area of a trapezoid calculated?

The area of a trapezoid is calculated using the formula ( \text{Area} = \frac{1}{2} \times (b_1 + b_2) \times h ), where ( b_1 ) and ( b_2 ) represent the lengths of the two parallel bases, and ( h ) is the height—the perpendicular distance between the bases.

This formula works because the trapezoid can be considered as having two bases that are of different lengths. By averaging the lengths of the two bases (using ( \frac{1}{2} \times (b_1 + b_2) )), you are effectively finding the length of a rectangle that has the same height as the trapezoid, allowing you to calculate the area more accurately. The multiplication by the height ensures that you account for the vertical dimension, which is critical in determining the overall size of the trapezoid.

Therefore, this formula captures the essential geometric properties of trapezoids, allowing for an accurate computation of their area.