Find the area of the regular polygon with the given radius. The radius of the square is 6 cm. area= apothem x perimeter/ 2
See 12:52am post.
To find the area of a regular polygon, you'll need to know the length of the apothem and the perimeter of the polygon. The formula you mentioned, "area = apothem x perimeter / 2", is correct.
However, it's important to note that a square is not a regular polygon, as a regular polygon requires all sides and angles to be equal. A square is a special type of rectangle where all sides are equal and all angles are 90 degrees.
Nonetheless, to find the area of a square with a given radius of 6 cm, you can follow these steps:
1. Start by finding the perimeter of the square. Since all sides of a square are equal, you can multiply the length of one side by 4. In this case, the length of one side is twice the radius, so the perimeter is 4 * 6 cm = 24 cm.
2. Next, find the apothem of the square. The apothem is defined as the perpendicular distance from the center of the square to one of its sides. For a square, the apothem is equal to half the side length, which is half the radius in this case. So, the apothem is 6 cm / 2 = 3 cm.
3. Now, substitute the values of the apothem (3 cm) and perimeter (24 cm) into the formula for the area of a polygon: area = apothem x perimeter / 2.
area = 3 cm * 24 cm / 2
= 72 cm^2
Therefore, the area of the square with a radius of 6 cm is 72 square centimeters.