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In the given figure, radius of a circle is 14√2 cm. PQRS is a square. EFGH, ABCD, WXYZ and LMNO are four identical squares. What is the total area (in cm2) of all the small squares?

In the given figure, radius of a circle is 14√2 cm. PQRS is a square. EFGH, ABCD, WXYZ and LMNO are four identical squares. What is the total area (in cm2) of all the small squares? Correct Answer 125.44

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Given:

r = 14√2 cm

Calculation:

Diameter = 2 × radius = 28√2 cm

∴ Side of larger square = Diameter/√2 = 28 cm

∴ TO = 14 cm

Here OX = OU = 14√2

Let the side of smaller square VT = a cm

So, VX = a/2 cm

∴ VO = 14 + a

In ΔOVX;

OX2 = VX2 + VO2

⇒ 392 = a2/4 + (14 + a)2

⇒ 392 = a2/4 + 196 + a2 + 28a

⇒ 5a2/4 + 28a – 196 = 0

⇒ 5a2 + 112a – 784 = 0

⇒ a = 5.6 cm

∴ The total area of all the small squares = 4 × 5.6 × 5.6 = 125.44 cm2

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