图中显示圆心为 $O$ 的圆的扇形 $OAB$。弧 $AB$ 的长为 $8\text{ cm}$。已知扇形的周长为 $20\text{ cm}$。

(a) 求阴影弓形的周长。

(b) 求阴影弓形的面积。

Answer all questions. You should use a calculator where appropriate.

You must show all necessary working clearly; no marks will be given for unsupported answers from a calculator.

Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question.

请回答所有题目。适当时应使用计算器。必须清楚展示所有必要的计算过程；仅给出计算器答案而没有过程，不予评分。除非题目另有精度要求，非精确数值答案保留 3 位有效数字，以度为单位的角度保留 1 位小数。

从扇形周长扣掉弧长得到两条半径。用弧长求圆心角，再平分等腰三角形求弦长。

Since $8+2r=20$, we have $r=6$ cm. The central angle is $8/6=4/3$ radians. Bisecting the angle at $O$ gives the half-chord $6\sin(2/3)$, so the segment perimeter is

to three significant figures.

阴影是扇形减去由两条半径和弦组成的三角形。

The area in square centimetres is

or $6.51\,\mathrm{cm}^2$ to three significant figures.