The figure above is constructed by separating a circular region into 6 equal parts and rearranging the parts as shown. If the diameter of the circle is d, what is the perimeter of the figure above?

Source | OGQR 2020 |

Type | Problem Solving |

Topic | Geometry |

Sub-Topic | Circle |

Difficulty | Medium – Hard |

### Solution

__Given__

__Given__

In this question, we are given

- A diagram, which is constructed by separating a circular region into 6 equal parts and rearranging them, as shown in the diagram.
- The diameter of the circle is d.

__To Find__

__To Find__

We need to determine

- The perimeter of the figure, as shown.

__Approach & Working__

__Approach & Working__

The perimeter of the given figure consists of 2 parts:

- 6 equal length arcs, which together form the perimeter of the circle
- 2 equal line segments, each of which is equal to the radius of the circle

The total length of the 6 arcs = the perimeter of the circle = 2π * (d/ 2) = πd

The total length of the 2 line segments = (d/ 2) + (d/ 2) = d

- Therefore, the perimeter of the given figure = πd + d

Hence, the correct answer is option D.

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