429,850 views
9 votes
9 votes
Diagram 9 shows a piece of floor tiles centre at O

Diagram 9 shows a piece of floor tiles centre at O-example-1
User Noliv
by
2.4k points

1 Answer

23 votes
23 votes

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,


undefined

User Relekang
by
2.7k points