Answer: 200 square units
Step-by-step explanation:
Given
Circumference of the circle is [tex]20\pi[/tex]
Suppose r is the radius of the circle
The biggest area of a quadrilateral that can fit in a circle is of square.
Deduce the radius of the circle
[tex]2\pi r=20\pi\\r=10\ \text{units}[/tex]
Suppose the side of the square is a
from the figure, we can write
[tex]\Rightarrow a^2+a^2=(2r)^2\\\Rightarrow 2a^2=4r^2\\\Rightarrow a=\sqrt{2}r\\\Rightarrow a=10\sqrt{2}\ \text{units}[/tex]
Area of the quadrilateral is
[tex]\Rightarrow A=(10\sqrt{2})^2\\\Rightarrow A=100\times 2\\\Rightarrow A=200\ \text{square units}[/tex]
