Calculate Parallelogram Area: Using Circle Diameter 10π cm and Rhombus Area 24 cm²

The parallelogram ABCD is shown below.

BC is the diameter of the circle whose circumference is equal to $10\pi$ cm.

ECFD is a rhombus whose area is 24 cm².

What is the area of ABCD?

Let's try to calculate the area in two ways.

In the first method, we will try to use the rhombus ECFD:

Let's try to calculate according to the formula $area=DC\times h_{DC}$

We will lower a height to DC and see that we do not have enough data to calculate, so we will not be able to calculate the area of the parallelogram using the rhombus.

In the second method , we will try to use the circle:

$area=BC\times h_{BC}$We will lower a height to BC and see that we do not have enough data to calculate, so we will not be able to calculate the area of the parallelogram using the circle.

From this it follows that we do not have enough data to calculate the area of parallelogram ABCD and therefore the exercise cannot be solved.