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 small squares?

Solution (By Examveda Team)

Side of square PQRS
$$\eqalign{ & = \frac{{{\text{Diameter of circle}}}}{{\sqrt 2 }} \cr & = \frac{{14\sqrt 2 \times 2}}{{\sqrt 2 }} \cr & = 28{\text{ cm}} \cr} $$

In ΔABO
AB = a
OB = 14√2
AO = 14 + 2a
OB² = AB² + OA²
(14√2)² = a² + (14 + 2a)²
196 × 2 = a² + 196 + 4a² + 56a
5a² + 56a - 196 = 0
5a² + 70a - 14a - 196 = 0
5a(a + 14) - 14(a + 14) = 0
(a + 14)(5a - 14) = 0
a = -14, a = $$\frac{{14}}{5}$$
Side of small square = 2a = $$\frac{{28}}{5}$$
Required Area $$ = 4 \times {\left( {\frac{{28}}{5}} \right)^2} = 125.44{\text{ c}}{{\text{m}}^2}$$