This polynomial would simplify to A = (1/2) × (2x + 6) × (x - 11) or A = (x + 3) × (x - 11).
The area polynomial formula for a trapezoid changes when the longer base is extended by 1 foot, affecting the percent of change calculation. For a magnified trapezoid with specific base and height values, the area polynomial can be specifically calculated and simplified.
In hockey, the area of the trapezoidal region behind the goal where a goalie can play the puck is important. If the longer base of the trapezoid is extended by 1 foot, and the shorter base remains 22 feet, the polynomial representing the area of this trapezoid will change as follows:
Original area formula for a trapezoid: A = (1/2) × (b1 + b2) × h
New area formula with extended base: A' = (1/2) × (b1 + (b2 + 1)) × h
To find the percent of change in the area, you would calculate the difference between the new area and the original area, and then divide by the original area, finally multiply by 100 to get the percentage:
Percent of change = ((A' - A) / A) × 100%
For a trapezoid magnified such that the bases are x feet and x + 6 feet with the distance between the parallel sides as x - 11 feet,
The area polynomial changes to: A = (1/2) × (x + (x + 6)) × (x - 11)