Question

PLEASE HELP ASAP!!!! Thanks!!

Answer 1

Answer:

1.2 cm

Step-by-step explanation:

Quadrilateral circumscribing a circle is a quadrangle whose sides are tangent to a circle inside it (see attached diagram).

The area of circumscribed quadrilateral is

$A=p\cdot r,$

where $p=\dfrac{a+b+c+d}{2}$ is semi-perimeter and r is radius of inscribed circle.

In your case, $A=12\ cm^2$

If a quadrilateral is circumscribed over the circle, then the sum of opposite sides is equal, so

$a+c=b+d=10\ cm,$

so

$P=10+10=20\ cm\\ \\p=\dfrac{20}{2}=10\ cm$

Now

$12=10\cdot r\Rightarrow r=\dfrac{12}{10}=1.2\ cm$