Question

In the Figure, four quadrants are touching each other at the points P, Q, R and S. The radius of each is 7cm. Find the area of the shaded region.

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Solution :

It is given that ,

Radius of the each quadrant ( r ) = 7cm

central angle ( x ) = 90°

i ) Area of each quadrant = (x/360)×πr²

= ( 90/360 ) × ( 22/7 ) × 7²

= ( 22 × 7 )/4

= 154/4 cm² ----( 1 )

ii ) Area of 4 such quadrants = 4 × 144/4

= 154 cm² -----( 2 )

iii ) Side of a square ( a ) = 2r

=> a = 2 × 7 = 14 cm

Area of the square = a²

= ( 14 cm )²

= 196 cm² ----( 3 )

iv ) Area of the shaded region

= ( 3 ) - ( 2 )

= 196 cm² - 154 cm²

= 42 cm²

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Or

Area of the shaded region

= Area of the square - area of the circle

[ Four equal quadrants makes a circle ]

= a² - ( πr² )

= 14² - ( 22/7 ) × 7²

= 196 - 154

= 42 cm²


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