### 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 =

22 |

7 |

**Answer:**

55 sq. m.

**Step by Step Explanation:**

- Let's name the outer square as ABCD, and the inner square as PQRS as shown below:

- If the radius of the circle is R, the side of the outer square will be double of circle's radius:

AB = 2R - Area of outer square,

Area(ABCD) = 2R × 2R = 4R^{2} - Side of the inner square PQRS can be calculated using Pythagoras Theorem:

PQ = ^@ \sqrt {R^2 + R^2} ^@

or, PQ = √2R - Area of inner square,

Area(PQRS) = √2R × √2R = 2R^{2} - The difference in areas of the two squares is given to be 35 sq. m.

Thus, Area(ABCD) - Area(PQRS) = 35

⇒ 4R^{2}- 2R^{2}= 35

⇒ 2R^{2}= 35

⇒ R^{2}=35 2 - Now that we know the radius of the circle, we can calculate the area of the circle using the formula,

Area(circle) = πR^{2}

=

×22 7 35 2

= 55 sq. m.