if the are of the circumcircle of an equilater triangle be 616 sq.m..,then hight of the triangle is.??
draw an altitude. It forms a 30-60-90 right triangle, where the sides are in the ratio
1:√3:2
Well, aren't equilateral triangles just the life of the party? Let's have some fun with math, shall we?
To find the height of an equilateral triangle, we have to rely on our friend Pythagoras. You know, the guy with the theorem. But before we get into that, let's find the length of each side of our triangle.
Since the area of the circumcircle (the circle that goes through all three vertices of the equilateral triangle) is 616 sq.m, we can use that information to find the radius of the circle. The formula for the area of a circle is A = πr². So, dividing the area by π gives us the radius squared.
616 / π ≈ 196.203
Now, since an equilateral triangle is made up of three congruent sides, the radius of the circumcircle is also equal to the height of the triangle. So, we can say that the height is √196.203.
Drumroll, please!
√196.203 is approximately 14.009 meters.
So, the height of the equilateral triangle is about 14.009 meters. Keep in mind that I'm rounding, so don't go measuring this with a microscope, okay?
To find the height of the equilateral triangle, we can use the formula:
Area of equilateral triangle = (sqrt(3)/4) * side^2
Given that the area of the circumcircle is 616 sq.m, we can use the formula for the area of the circumcircle (π * diameter^2 / 4) to find the diameter.
Area of circumcircle = π * diameter^2 / 4
616 = π * diameter^2 / 4
To find the diameter, we multiply both sides by 4/π:
4/π * 616 = diameter^2
Diameter = sqrt(4/π * 616)
Once we have the diameter, we can find the side length of the equilateral triangle by dividing the diameter by √3:
Side length = diameter / √3
Finally, to find the height of the triangle, we can use the formula h = (√3/2) * side length:
Height = (√3/2) * side length
Therefore, once we know the area of the circumcircle is 616 sq.m, we can use these formulas to find the height of the equilateral triangle.
To find the height of an equilateral triangle, we need to use the formula for the area of an equilateral triangle:
Area = (sqrt(3) / 4) * s^2
where s is the length of the side of the equilateral triangle.
In this case, we are given the area of the circumcircle of the triangle as 616 sq.m. The circumcircle of an equilateral triangle is a circle that passes through all three vertices of the triangle.
The formula for the area of a circle is:
Area = π * r^2
where r is the radius of the circle.
For an equilateral triangle, the radius of the circumcircle is equal to the length of the side of the triangle divided by the square root of 3:
r = s / sqrt(3)
Given that the area of the circumcircle is 616 sq.m., we can set up the equation:
π * (s / sqrt(3))^2 = 616
Simplifying the equation, we have:
π * s^2 / 3 = 616
Now we can solve for s by rearranging the equation:
s^2 = (616 * 3) / π
s = sqrt((616 * 3) / π)
Once we have the length of the side of the equilateral triangle, we can find the height using the formula:
Height = (sqrt(3) / 2) * s
Height = (sqrt(3) / 2) * sqrt((616 * 3) / π)
Calculating the above expression will give us the height of the equilateral triangle.