Answer:
The perimeter of the regular polygon is 33 cm, and the area is 297.75 square cm.
Step-by-step explanation:
A regular polygon is a polygon with all sides and angles equal. To find the perimeter of a regular polygon, we simply multiply the length of one side by the number of sides. In this case, we have a regular polygon with 11 sides, and each side has a length of sqrt(3) cm. Therefore, the perimeter is 11 * sqrt(3) = 33 cm.
To find the area of a regular polygon, we need to use the formula A = (1/2) * P * apothem, where A is the area, P is the perimeter, and apothem is the distance from the center of the polygon to the midpoint of a side. The apothem of a regular polygon can be found using the formula apothem = (side length) / (2 * tan(180/n)), where n is the number of sides.
In this case, the apothem is (sqrt(3)) / (2 * tan(180/11)) cm ≈ 5.416 cm. Therefore, the area is (1/2) * 33 * 5.416 = 297.75 square cm.