To find the perimeter of a quarter of a circle, we need to find the length of the curved part of the quarter circle and add it to the length of the two straight sides.

The length of the curved part of the quarter circle is equal to one-fourth of the circumference of the full circle. The formula for the circumference of a circle is C = 2πr, where C is the circumference and r is the radius.

In this case, the radius is 10 cm, so the circumference of the full circle is C = 2π(10) = 20π cm.

To find the length of the curved part of the quarter circle, we divide the circumference by 4: 20π/4 = 5π cm.

The length of the two straight sides is equal to the radius, which is 10 cm.

Therefore, the perimeter of the quarter circle is 5π cm + 10 cm + 10 cm = 5π cm + 20 cm.

The perimeter of the quarter of the circle is 5π cm + 20 cm.