Quarter-Circle Perimeter

Quarter-circle perimeter: how to solve

A quarter circle is one fourth of a full circle. Its perimeter is made of two parts:

1. the two straight sides, which are the radii
2. the curved arc, which is one fourth of the circle’s circumference

Step-by-step method

1. Identify the radius from the problem.

2. Find the arc length of the quarter circle:

   [ \text{arc} = \frac{1}{4}(2\pi r)=\frac{\pi r}{2} ]

3. Add the two radii:

   [ r+r=2r ]

4. Write the perimeter:

   [ P=2r+\frac{\pi r}{2} ]

5. Simplify the final answer as much as possible. Leave the answer exact if (\pi) is present, unless a decimal is requested.

Quick check

Make sure your result includes both the straight edges and the curved part. If the answer looks too small, you may have forgotten one radius or used the full circumference instead of one fourth of it.