Question

ABCD is a square of side 14 cm. four congruent circles are drawn in the square as shown in fig. calculate the area of the shaded region
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Answer 1

Step-by-step explanation:

Since, all angles of square are 90°.

Therefore, Area of shaded region = (Area of Square - Area of 4 quadrants of circles)

Now, Area of Square = Side×Side

= (14×14) cm2

= 196 cm2

Since, the circles are congruent.

Therefore, radius of all the circles are equal.

Side of square is also 2 × radius of 2 circles.

And since the radius of all the circles are equal.

So, 2 × radius = diameter

=> radius = 14/2

= 7 cm

Area of 1 quadrant = 1/4×πr^2

= 1/4 × 22 × (7)^2

= (1/4 × 22 × 49) cm2

= 154/4 cm2

Area of 4 quadrants = 4 × Area of 1 quadrant

= 4 × 154/4 cm2

= 154 cm2

Area of shaded region = (Area of Square - Area of 4 quadrants of circles)

= (196-154) cm2

= 42 cm2

Hope it helps :)

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