Find the perimeter and area of a sector of a circle with a radius of 15 cm if the arc of the sector contains 54 degrees.

Using the formula l = 2πr, where l is the circumference, r is the radius of the circle, π is the number pi, we find the length of this circle.
According to the condition of the problem, the radius of this circle is 15 cm, therefore, the circumference l is:
l = 2π * 15 = 30π cm.
Using the formula S = πr ^ 2, where S is the area of ​​the circle, r is the radius of the circle, π is the number pi, we find the area of ​​this circle:
S = π15 ^ 2 = 225π cm ^ 2.
Find the perimeter and area of ​​the sector.
By the condition of the problem, the arc of the sector contains 54 °.
Since the entire circle contains 360 °, and the circumference is 30π cm, the arc length of the sector is 30π * 54/360 = 4.5π cm.
Therefore, the sector perimeter is:
15 + 15 + 4.5π = 30 + 4.5π cm.
The sector area is:
S * 54/360 = 225π * 54/360 = 33.75π cm ^ 2.
Answer: the perimeter of the sector is 30 + 4.5π cm, the area of ​​the sector is 33.75π cm ^ 2.