In the given figure, ABCD is a square, EFGH is a square formed by joining mid points of sides of ABCD. LMNO is a square formed by joining mid points of sides of EFGH. A circle is inscribed inside EFGH. If area of circle is 38.5 cm², then what is the area (in cm²) of square ABCD ?

Solution (By Examveda Team)

Area of circle = 38.5
πr² = 38.5
r² = $$\frac{{385}}{{10}} \times \frac{7}{{22}}$$
r = $$\frac{7}{2}$$ cm
MN = 2r = 7 cm

$${\sqrt 2 }$$ a = 7 cm
a = $$\frac{7}{{\sqrt 2 }}$$ cm
Side of square EFGH = 2 × a
EG = 7$${\sqrt 2 }$$ cm

$${\sqrt 2 }$$ b = 7$${\sqrt 2 }$$
b = 7 cm
Side of square ABCD = 7 × 2 = 14 cm
Area = a² = 14² = 196 cm²