### Given a circle, a circumscribed square is one that completely encloses the circle, and an inscribed square is one that is completely enclosed by the circle, as shown below:If the the difference in the areas of the two squares is 35 sq. m., then what is the area of the circle? (Assume π =  227  )

55 sq. m.

Step by Step Explanation:
1. Let's name the outer square as ABCD, and the inner square as PQRS as shown below:
2. If the radius of the circle is R, the side of the outer square will be double of circle's radius:
AB = 2R
3. Area of outer square,
Area(ABCD) = 2R × 2R = 4R2
4. Side of the inner square PQRS can be calculated using Pythagoras Theorem:
PQ = $\sqrt {R^2 + R^2}$
or, PQ = √2R
5. Area of inner square,
Area(PQRS) = √2R × √2R = 2R2
6. The difference in areas of the two squares is given to be 35 sq. m.
Thus, Area(ABCD) - Area(PQRS) = 35
⇒ 4R2 - 2R2 = 35
⇒ 2R2 = 35
⇒ R2 =
 35 2

7. Now that we know the radius of the circle, we can calculate the area of the circle using the formula,
Area(circle) = πR2
=
 22 7
×
 35 2

= 55 sq. m.