Payal Tandon
Co-founder, e-GMAT
Welcome to e-GMAT Support!
I am Payal, Co-Founder of e-GMAT.
Feel free to ask any Query.
We will be contacting you soon on

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

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

We need to determine

• The perimeter of the figure, as shown.

#### 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.

If you are planning to take the GMAT, we can help you with a personalized study plan and give you access to quality online content to prepare. Write to us at acethegmat@e-gmat.com. We are the most reviewed GMAT prep company on gmatclub with more than 2400 reviews and are the only prep company that has delivered more than 700+ scores than any other GMAT club partner. Why don’t you take a free trial and judge for yourself?