Question

Diagram 9 shows a piece of floor tiles centre at O

Answer 1

Notice that the perimeter in the figure consists of 2 sides equal to the radius of the circle and the arc that corresponds to a fraction of a whole circumference of a 14 cm radius.

`\begin{gathered} P=14+14+\text{arc} \\ \text{and} \\ P=39 \\ \Rightarrow\text{arc}=39-14-14=11 \\ \Rightarrow\text{arc}=11 \end{gathered}`

And,

`\begin{gathered} \text{arc}=2\pi r((\theta)/(2\pi)) \\ \Rightarrow\text{arc}=r\theta \\ \Rightarrow\theta=(arc)/(r)=(11)/(14) \end{gathered}`

Where theta is in radians.

The area of an arc is given by the equation:

`A_{\text{arc}}=r^2\pi((\theta)/(2\pi))`

Finally,