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Cutting the equilateral triangle in half results in two right triangles each with a base of length x/2, and angles of 30, 60, and 90 degrees. Using the lengths of sides of a 30-60-90 triangle it can be found that the height is (x/2)√(3), which is the same as the height of the equilateral triangle.
So the height of the equilateral triangle is x√(3) / 2.
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If x be the length of a median of an equilateral triangle then its area is?
30
What is the perimeter of an equilateral triangle with an altitude of 15?
An equilateral triangle has 3 equal interior angles each of 60 degrees. There are two right angled triangles in an equilateral triangle. So we can use trigonometry to find the length of one side of the equilateral triangle then multiply this by 3 to find its perimeter. Hypotenuse (which is one side of the equilateral) = 15/sin 60 degrees = 17.32050808 17.32050808 x 3 = 51.96152423 Perimeter = 51.96152423 units.
What is the equation for the volume of a triangular prism?
The area of the cross section (the triangle) muliplied by the length of the prism. Area of triangle= 0.5 x base x height Then mulitply by the length the prism goes back
Area of a triangle base of 10 and a height of 15?
The area of a triangle is (1/2) x (length of the base) x (height of the triangle). You ought to be able to handle it from this point.
What is the altitude of an equilateral triangle if its perimeter is 15?
the height is 4.33 units cos 30 = .866 15 / 3 = 5 5 x .866 = 4.33
What is the formula for the area for an equilateral triangle?
-- The area of any triangle is 1/2 (length of the base x height). -- For an equilateral triangle, that's equivalent to 1/2 x sqrt(3) x (length of a side).
How do l work out the area of an equilateral triangle?
0.5 x base length x vertical height
What is the area of an equilateral triangle of side 2a?
The height of an equilateral triangle is √3/2 x side_length. So for an equilateral triangle of side length 2a, the area is: area = 1/2 x base x height 1/2 x (2a) x (√3/2 x 2a) = √3 a2
How do you find the function that models the area A of an equilateral triangle in terms of the length X of one of its sides?
The area of any triangle is (1/2) x (the base) x (the height). If the length of the side of the equilateral triangle is 'X', then its height is (X/2) x sqrt(3). Its area is then (1/2) x (X) x [ (X/2) x sqrt(3) ] = X2sqrt(3) / 4
What height is an equilateral triangle with sides measuring 3cm?
Height of an equilateral triangle = √3 / 2 x side = (√3 / 2 ) x 3 = 2.598 cm.
What is the height of an equilateral triangle with sides of 20?
Height of an equilateral triangle = √3/2 x side = √3/2 x 20 = 10√3 ≈ 17.32
How do you find the height of an equilateral triangle if you have the length of the hypotenuse?
An equilateral triangle hasn't a hypotenuse; hypotenuse means the side opposite the right angle in a right triangle. An equilateral triangle has no right angles; rather all three of its angles measure 60 degrees. Knowing the length of the hypotenuse of a right triangle does not give enough information to determine the triangle's height. But the length of a side (which is the same for every side) of an equilateral triangle is enough information from which to calculate the height of that triangle. The first way is simply to use the formula that has been developed for this purpose: height = (length X sqrt(3)) / 2. But you can also use the geometry of right triangles to solve for the height. That is because you can bisect the triangle with a vertical line from the top vertex to the center of the base. The length of that line, which splits the equilateral triangle into two right triangles, is the height of the equilateral triangle. We know a lot about each right triangle formed by bisecting the equilateral triangle: * - The hypotenuse length is the length of the equilateral triangle's side. * - The base length is half the length of the hypotenuse. * - The angle opposite the hypotenuse is 90 degrees. * - The angle opposite the vertical is 60 degrees (the measure of every angle of any equilateral triangle). * - The angle opposite the base is 30 degrees (half of the bisected 60-degree angle). * - (Note that the sum of the angles does equal 180 degrees, as it must.) Now to solve for the height of a right triangle. There are a few ways. For labeling, let's let h=height of the equilateral triangle and the vertical side of the right triangle; A=every angle of the equilateral triangle (each 60o); s=side length of any side of the equilateral triangle and thus the hypotenuse of the right triangle. Since the sine of an angle of a right triangle is equal to the ratio of the opposite side divided by the hypotenuse, we can write that sin(A) = h/s. Solving for h, we get h=sin(A)/s. With trig tables you can now easily find the height.
If x be the length of a median of an equilateral triangle then its area is?
30
What is Height in an equilateral triangle?
let the side be x...the height is (sq.root of 3)/2 multiplied by x
What is the length of the altitude of an equilateral triangle if one side has a length of 6 cm?
6 squared = 3 squared + x squared if x is the height (altitude) of the triangle 36 = 9+x squared x squared =27 so x = 3 sqrt3 = 5.19615
How long are each sides of an equilateral triangle if the perimeter is 60?
20. There are 3 sides to any triangle. For an equilateral triangle all 3 sides are the same length. Therefore for this triangle we can say that, where x equals the length of a side: 3x = 60 x = 60/3 x = 20
How do you find the height of an equilateral triangle if you don't know its area and you only know that each side is equal to 41.3m?
Cut it exactly down the middle, along its height, and put one piece aside. The remaining side is a right triangle. The slanting side of the right triangle is a whole side of the original equilateral triangle, the bottom is half of an original side, and the vertical line is the height of the original triangle. Now you have a right triangle and you know the lengths of two of its sides, so you use what you know about right triangles to find the length of the third side, which is the height of the original equilateral triangle. It turns out to be 0.866 times the side of the equilateral triangle. (rounded) Technically, that's (1/2) x (side) x sqrt(3)
