8 On television a weather forecaster uses a cloud symbol shown in the diagram. Its perimeter consists of a straight line AE, two semicircular arcs APB and DQE and the major arc BRD of a circle, centre C. AE = 7.5 cm, AB = DE = 3 cm and BC= CD = 2.8 cm. Angle BAE = angle DEA = 70° and X is the midpoint of BD. [For π, use either your calculator value or 3.142.] (a) (i) Use the trapezium ABDE to show that BX = 2.724 cm. [4] (ii) Calculate angle BCX. [2] (b) Calculate (i) the area of triangle BCD, [3] (ii) the area of the trapezium ABDE, [4] (iii) the area of the major sector BCD, [3] (iv) the to

Question

8 On television a weather forecaster uses a cloud symbol shown in the diagram. Its perimeter consists of a straight line AE, two semicircular arcs APB and DQE and the major arc BRD of a circle, centre C. AE = 7.5 cm, AB = DE = 3 cm and BC= CD = 2.8 cm.  Angle BAE = angle DEA = 70° and X is the midpoint of BD. [For π, use either your calculator value or 3.142.] (a) (i) Use the trapezium ABDE to show that BX = 2.724 cm. [4] (ii) Calculate angle BCX. [2] (b) Calculate (i) the area of triangle BCD, [3] (ii) the area of the trapezium ABDE, [4] (iii) the area of the major sector BCD, [3] (iv) the to