Huntington wants to estimate the area of a trapezoid shape stage each square represents one square foot the designer decides to find the area by composing a rectang le what is the length of the base of the rectangle and feet
To compose a rectangle from the trapezoid, the designer would need to add a rectangular piece to the shorter base of the trapezoid to make it a rectangle.
Let's denote the shorter base of the trapezoid as 'b', the longer base as 'B', and the height as 'h'.
The area of a trapezoid is calculated as (1/2)*(b + B)*h.
To create a rectangle with the same area, we can calculate the longer side of the rectangle by taking into account the extra area added as a rectangle. Let the length of the base of the rectangle be 'x'.
So, ((1/2)*(b + B)*h) + ((B - b)*h) = x*h
This simplifies to: ((B + b)/2) + B - b = x
Given that each square represents one square foot, the bases are likely to be whole numbers.
Let's assume the shorter base 'b' be 10 feet. Let us also assume that the area is 100 square feet.
Plugging in the values: ((10 + B)/2) + B - 10 = 100
5 + B + B - 10 = 100
2B - 5 = 100
2B = 105
B = 105/2
B = 52.5
Therefore, the length of the base of the rectangle would be 52.5 feet.