Question

In the given figure, PQ = 24, PR = 7 cm and O is the centre of the circle. Find the area of the shaded region.

Answer 1

In the right ΔRPQ, we have:

`"RQ" = sqrt("RP"^2 + "PQ"^2)`

         `=sqrt(7^2+24^2)`

         `= sqrt(49+576)`

          = 25 cm

  OR = OQ = 12.5 cm

Now,

Area of the circle = πr² 

= 3.14 × 12.5 × 12.5

= 490.625 sq. cm

Area of the semicircle `= 490.625/2 = 245.31  "sq.cm" `

Area of the traingle `= 1/2xx"b"xx"h" = 1/2xx7xx24=84  "sq.cm"`

Thus, we have

Area of the shaded part = Area of the semicircle - Area of the triangle]

= 245.13 - 84 

= 161.31 cm²