Answer:
the length of DC is (3/8) times the area of the trapezium.
Explanation:
Unfortunately, there is no attached diagram to your question. Without a diagram, it is difficult to provide a specific solution. However, I can give you some general information that may help you solve the problem.
A trapezium is a quadrilateral with at least one pair of parallel sides. In this case, we know that AB is one-third of DC, so AB is shorter than DC. The vertical distance between YAB and DC is given as 12cm. This means that the height of the trapezium is 12cm.
To find the length of DC, we need to use the formula for the area of a trapezium:
Area = (1/2) x (sum of parallel sides) x (height)
In this case, we know that the area of the trapezium is b m², and we can represent the length of DC as x. We also know that AB is one-third of DC, so we can represent AB as (1/3)x.
Substituting these values into the formula, we get:
b = (1/2) x [(1/3)x + x] x 12
Simplifying this equation, we get:
2b = (4/3)x x 12
2b = 16x/3
x = (3/16) x 2b
x = (3/8) b
So the length of DC is (3/8) times the area of the trapezium.