Circle P6 2009 SA2 P2 MGS Q18

18. The shaded part below is made up of a quarter circle and a semicircle which are drawn within the rectangle ACDF. AB = 12 cm.

a) Find the area of rectangle ACDF.

b) What percentage of rectangle ACDF is shaded? Round off your answer to 2 decimal places.

12 ÷ 2 = 6

6 + 12 = 18

18 x 12 = 216 cm²

a) The area of rectangle ACDF is 216 cm².

1/4 x 22/7 x 12 x 12 = 113 1/7

1/2 x 22/7 x 6 x 6 = 56 4/7

113 1/7 – 56 4/7 = 56 4/7

                         ≈ 56.57 cm²

56 4/7 ÷ 216 x 100% = 26.19%

b) 26.19% of rectangle ACDF is shaded.