Quadrilateral $abcd$ is a trapezoid with $ab$ parallel to $cd$. we know $ab = 20$ and $cd = 12$. what is the ratio of the area of triangle $acb$ to the area of the trapezoid $abcd$? express your answer as a common fraction.

Draw a diagram to illustrate the problem as shown below.

The area of triangle acb is

A₁ = (1/2) * 20*h = 10h

The area of trapezoid abcd is

A₂ = (1/2) * (20+12) * h = 16h

The ratio A₁/A₂ is

A₁/A₂ = (10h) / (16) = 5/8

Answer:

The ratio of triangle acb to the area of trapezoid abcd is 5/8.