Question 3 – 5.3 Areas of Sectors and Segments - Questions

An architectural blueprint for a plaza features a circular water fountain and a stone promenade. The fountain area is defined by a major sector $A B C O A$ of a circle with centre $O$ , while the promenade is a triangle $A O D$ adjacent to it. The following information is given:

The radius of the fountain is $12\text{ m}$
The edge of the promenade $A D$ has a length of $m25\text{ m}$
The angle $∠ODA\angle ODA$ at the far end of the promenade is $radians0.35\text{ radians}$
The angle $∠AOD\angle AOD$ is obtuse
The points $O$ , $C$ , and $D$ lie on a straight line

The major sector $A B C O A$ has an arc $A B C$ that starts at $C$ and ends at $A$ .

Find:

the size of angle $∠AOD\angle AOD$ , in radians, to 3 decimal places,

the length of the arc $A B C$ of the fountain, in metres, to one decimal place,

the total area of the plaza feature (fountain and promenade), in $m2\text{m}^2$ , to one decimal place.

The radius of the fountain is $12\text{ m}$
The edge of the promenade $A D$ has a length of $m25\text{ m}$
The angle $∠ODA\angle ODA$ at the far end of the promenade is $radians0.35\text{ radians}$
The angle $∠AOD\angle AOD$ is obtuse
The points $O$ , $C$ , and $D$ lie on a straight line