The sum of the lengths of two opposite sides of the circumscribed quadrilateral is 12 cm, the length of a radius of the circle is 5 cm. Find the area of the quadrilateral

60cm^2

Step-by-step explanation:

We assume that is a circumscribing quadrilateral, rather than one that is circumscribed. It is also called a "tangential quadrilateral" and its area is ...

 K = sr

where s is the semi-perimeter, the sum of opposite sides, and r is the radius of the incircle.

 K = (12 cm) (5cm) = 60 cm²

A quadrilateral can only be tangential if pairs of opposite sides add to the same length. Hence the given sum is the semiperimeter.

it would rotate about 180 degrees.

(5x-1)^2= (5x)^2-2(5x)×1+(1)^2=25x^2-10x+1