Question

Find the area of circular path(shaded region), if in rectangle ABCD and PQRS, AB=PQ=10 cm, BC= 6 cm, BQ=RC=AP=SD= 1 cm. (take $\pi$=3.14)

• A. 31.4 $c{m}^2$
• B. 35.7 $c{m}^2$
• C. 62.8 $c{m}^2$
• D. 82.8 $c{m}^2$

Answer 1

The correct option is B 35.7 $c{m}^2$

QR=PS= BC-BQ-CR = 6-1-1 = 4 cm

Area of shaded region
= Area of rectangle ABCD
- Area of rectangle PQRS
+ Area of the ring

Area of rectangle = Length$\times$Breadth

Area of rectangle ABCD = AB$\times$AD
= 10$\times$6 = 60 $c{m}^2$
Area of rectangle PQRS = PQ$\times$QR
= 10$\times$4 = 40 $c{m}^2$

Area of ring = $\pi$$(R^2-r^2$)
.....(where R = $\frac{BC}{2}$ and r = $\frac{QR}{2}$)
= (3.14)$(3^2-2^2$) = 3.14$\times$(9-4)
= 3.14$\times$5 = 15.7

Area of shaded region = 60-40+15.7
= 20 + 15.7
= 35.7 $c{m}^2$