In the given figure, radius of a circle is 14 root 2 cm. PQRS is a square.
EFGH, ABCD, WXYZ and LMNO are four identical squares. What is the total area
(in cm^2) of all the small squares?
Answers
Given : Fig showing a circle of radius 14√2 cm. PQRS is a square.
To find : area of small circles
Step-by-step explanation:
PR = QS = Diameter = 2 * 14√2 = 28√2 cm
PR² = PQ² + QR² ( PQ = QR)
=> PQ = QR = RS = PS = 28 cm
Let say side of small square = x
in rectangle sides are 28 + x + x & x
Here diagonal again = Diameter = 28√2
=> (28 + 2x)² + x² = (28√2)²
=> 28² + 4x² + 112x + x² = 2 * 28²
=> 5x² + 112x - 28² = 0
=> 5x² + 140x - 28x - 28² = 0
=> 5x(x + 28) - 28(x + 28) = 0
=> (5x - 28)(x + 28) = 0
=> x = 28/5
=> x = 5.6
Area of one small square = (5.6)² = 31.36 cm²
Area of 4 small square = 4 *31.36 = 125.44 cm²
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