Arc DE has a length of ð(pie), and the straight line distance between points D and E is equal to the radius of the circle. What is the area of the circle?
To find the area of the circle, we need to know the radius. In this case, we are given that the straight line distance between points D and E is equal to the radius of the circle.
Let's denote the radius as r. Since the straight line distance between points D and E is equal to the radius, we can say that DE = r.
Now, the formula for the area of a circle is A = πr^2, where A is the area and r is the radius.
In our case, DE = r, so we can substitute it into the formula:
A = π(DE)^2.
Since DE = r, we can simplify it further:
A = π(r)^2.
Now, we can substitute ð (pi) for the value of π in the formula, as you mentioned that the arc DE has a length of ð (pi):
A = ð(r)^2.
Therefore, the area of the circle is ð (pi) times the square of the radius.