What is the area of a regular hexagon inscribed in a circle of diameter 8 inches?
the side = the radius for a hexagon.
so, area = 6 times the area of one equilateral triangle of side 4.
To find the area of a regular hexagon inscribed in a circle, you can use the formula:
Area of hexagon = (3√3/2) * s^2
where "s" is the length of one side of the hexagon.
In this case, the diameter of the circle is given as 8 inches. The radius of the circle, which is also the distance from the center of the circle to any of the vertices of the hexagon, can be found by dividing the diameter by 2:
Radius = Diameter / 2 = 8 / 2 = 4 inches.
Since the hexagon is regular, all the sides are equal in length. It can be divided into six congruent equilateral triangles. The side of each equilateral triangle is the same as the radius of the circle:
s = 4 inches.
Now, we can substitute the value of "s" into the formula to find the area of the hexagon:
Area of hexagon = (3√3/2) * s^2
Area of hexagon = (3√3/2) * (4^2)
Area of hexagon = (3√3/2) * 16
Area of hexagon = (3√3/2) * 16
Area of hexagon = 24√3 square inches.
Therefore, the area of the regular hexagon inscribed in a circle with a diameter of 8 inches is approximately 24√3 square inches.
To find the area of a regular hexagon inscribed in a circle, we can use the formula:
Area of hexagon = (3√3 / 2) * (side length)²
In this case, we are given the diameter of the circle, which is 8 inches. The radius of the circle is half the diameter, so the radius is 8 / 2 = 4 inches.
To find the side length of the hexagon, we can use the relationship between the side length and the radius in a regular hexagon. In a regular hexagon, the side length is equal to the radius.
So the side length of the hexagon is 4 inches.
Now we can substitute the side length into the formula to find the area:
Area of hexagon = (3√3 / 2) * (4 inches)²
Calculating the area, we have:
Area of hexagon = (3√3 / 2) * 16 square inches
Simplifying the expression:
Area of hexagon = (3√3 * 16 / 2) square inches
= (24√3) square inches
Therefore, the area of the regular hexagon inscribed in a circle with a diameter of 8 inches is 24√3 square inches.