Find the area of the regular polygon with the given radius. The radius of the square is 6 cm. area= apothem x perimeter/ 2
a = y = apothem.
X = b/2 = 6/2 = 3.
r = 6 cm.
X^2 + Y^2 = r^2.
3^2 + Y^2 = 6^2.
9 + Y^2 = 36.
Y = 5.2 cm = a.
P = N * L = 6 * 6 = 36 cm.
A = aP/2 = 5.2 * 36 / 2 = 93.6 cm^2.
Alternate Method:
A = 2.60r^2 = 2.60 * 6^2 = 93.6 cm^2.
HEX. only.
I'm sorry Henry, but that is wrong. The correct answer is actually 72.
I've done the complicated method with finding the apothem using the 45-45-90 triangle and then finding the side, and the perimeter. You'd have to substitute after that.
Thing is, the radius is also half of the diagonal. Meaning, the diagonal of this square would be 12. If the diagonal of the square of 12, the area is 72.
I hope this helps for anyone who sees this.
Well, the apothem of a square is actually equal to half of its side length, since the apothem is the distance from the center of the polygon to the midpoint of any side. So, in the case of a square with a radius of 6 cm, the apothem would be half of its side length, which is 6 cm as well.
Now we need to find the perimeter of the square. Since a square has all sides equal, we can simply multiply the side length by 4. So, the perimeter of the square is 6 cm x 4 = 24 cm.
Using the formula you provided, area = apothem x perimeter/2, we can plug in the values and calculate the area:
Area = (6 cm) x (24 cm) / 2 = 72 cm².
So, the area of the square with a radius of 6 cm is 72 square centimeters.
To find the area of a regular polygon, you can use the formula:
Area = apothem * perimeter / 2
In this case, the apothem is the distance from the center of the polygon to the midpoint of any one of its sides, and the perimeter is the sum of the lengths of all the sides.
Since we have a square and its radius is given, we need to find the apothem and perimeter of the square.
Apothem of a square:
In a square, the apothem is equal to half the length of any one of its sides. Since the radius is given as 6 cm, which represents half of a side, the length of one side of the square is 12 cm.
Perimeter of a square:
The perimeter of a square is calculated by multiplying the length of one side by 4. So, in our case, the perimeter of the square is 4 * 12 cm = 48 cm.
Now we have both the apothem and perimeter of the square. Let's substitute these values into the formula:
Area = apothem * perimeter / 2 = (6 cm) * (48 cm) / 2 = 288 cm^2
Therefore, the area of the square with a radius of 6 cm is 288 cm^2.