Question

In figure, arcs have been drawn with radii 14 cm each and with centres P, Q and R. Find the area of the shaded region.

Answer 1

Given that, radii of each arc (r) = 14 cm

Now, area of the sector with central angle P

= `(∠"P")/360^circ xx π"r"^2`

= `(∠"P")/360^circ xx π xx (14)^2 "cm"^2`  

Area of the sector with central angle Q

= `(∠"Q")/360^circ xx π"r"^2`

= `(∠"Q")/360^circ xx π xx (14)^2 "cm"^2`

And area of the sector with central angle R

= `(∠"R")/360^circ xx π"r"^2`

= `(∠"R")/360^circ xx π xx (14)^2 "cm"^2`

Therefore, sum of the areas of three sectors

= `(∠"P")/360^circ xx π xx (14)^2 + (∠"Q")/360^circ xx π xx (14)^2 + (∠"R")/360^circ xx π xx (14)^2`

= `π/360^circ xx (14)^2 xx [∠"P" + ∠"Q" + ∠"R"]`

= `π/360^circ xx 196 xx 180^circ` ...[Since, sum of all interior angles in any triangle is 180°]

= 98π

= `98 xx 22/7`

= 14 × 22

= 308

Hence, the required area of the shaded region is 308 cm².