Question

The area of a trapezoid is 66 sq units. The length of its longer base is 4 units longer than the length of its shorter base, and its height is 7 units longer than the length of its shorter base. Find the length of each base and the height of the trapezoid.

Answer 1

you know that with bases b and c, and height h, a trapezoid has area

a = h * (b+c)/2

Just plug in your numbers, letting x be the length of the short base:

a = (x+7) * (x + x+4)/2
66 = (x+7)(x+2)

x^2 + 9x - 52 = 0
(x+13)(x-4) = 0
x = 4

short base = 4
long base = 8
height = 11

area = 11(8+4)/2 = 11*6 = 66