\includegraphics{figure_4}
The triangle \(XYZ\) in Figure 4 has \(XY = 6\) cm, \(YZ = 9\) cm, \(ZX = 4\) cm and angle \(ZXY = a\).
The point \(W\) lies on the line \(XY\).
The circular arc \(ZW\), in Figure 4, is a major arc of the circle with centre \(X\) and radius 4 cm.
- Show that, to 3 significant figures, \(a = 2.22\) radians. [2]
- Find the area, in cm\(^2\), of the major sector \(XZWX\). [3]
The region, shown shaded in Figure 4, is to be used as a design for a logo.
Calculate
- the area of the logo [3]
- the perimeter of the logo. [4]