Question

With vertices A, B and C of a triangle ABC as centres, arcs are drawn with radius

6 cm each in fig. If AB= 20 cm, BC= 48 cm and CA= 52 cm, then find the area of

the shaded region. (Use  = 3.14 )

Answer 1

hope this helps u.......

Answer 2

Solution:-

Area of Triangle = 1/2 × Base × Height

=> Area = 1/2 × 20 × 48

=> Area = 480 cm²

Now,

Area of Unshaded Region = Area of ( Sector1 + Sector2 + Sector3).

Area of Sector1 = A/ 360 * πr² ( Taken A in place of Theta). _________(1).

Area of Sector2 = A'/ 360 * πr² ______(2).

Area of Sector3 = A''/360 * πr² ______(3).

Adding Area of Sector1 , Sector2 & Sector3. we get,

Area ( Sector1 + Sector2 + Sector3) = (A/ 360 * πr²) + (A'/ 360 * πr²) + (A''/360 * πr²).

=> Area of Unshaded Region

=> [( A + A' + A'')/ 360] * πr²

=> [( 180)/360] * πr²

=> 1/2 * 3.14 * 6 * 6

=> 3.14 * 18

=> 56. 52 cm²

Now,

Area of Shaded Region = Area of Triangle - Area of All three Sector

=> 480 cm² - 56.52 cm²

=> 423.48 cm²

Hence, Area of Shaded Region is 423.48 cm².