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 ?

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 ?

Answer: Option B

Solution

Answer: Option B

Solution:

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