volume of equilateral triangle with and area of 6 sq inches and height of 15 inches
A triangle is one-dimensional and so doesn't have volume.
but a triangular pyramid does:
v = 1/3 Bh
Now just plug in your numbers.
30
To find the volume of an equilateral triangle, we need to first calculate the base of the triangle.
The equilateral triangle has an area of 6 square inches. The formula to calculate the area of an equilateral triangle is (sqrt(3)/4) * side^2, where "side" represents the length of one side of the triangle.
We can rearrange the formula to find the side length:
side = sqrt((4 * area) / (sqrt(3)))
Plugging in the given area of 6 square inches, we get:
side = sqrt((4 * 6) / sqrt(3))
= sqrt(24 / sqrt(3))
Next, the height of the triangle is given as 15 inches. Given that the triangle is equilateral, the height is also the perpendicular bisector of the base, forming a right angle triangle.
Using the Pythagorean theorem, we can find the base of the right-angled triangle:
base = sqrt(side^2 - (height^2 / 4))
Substituting the values, we get:
base = sqrt((24 / sqrt(3))^2 - (15^2 / 4))
= sqrt(((24^2) / (3)) - 56.25)
= sqrt(576 / 3 - 56.25)
= sqrt(192 - 56.25)
= sqrt(135.75)
Now that we have the base length, we can calculate the area of the equilateral triangle using the formula mentioned earlier:
area = (sqrt(3) / 4) * side^2
Substituting the values, we get:
area = (sqrt(3) / 4) * (sqrt(135.75))^2
= (sqrt(3) / 4) * 135.75
= (1.732 / 4) * 135.75
= 1.732 * 33.9375
= 58.6855 square inches
Since we have the base length and the height, we can now calculate the volume using the formula for a triangular prism:
volume = base * height * (1/2)
Plugging in the values, we get:
volume = sqrt(135.75) * 15 * 0.5
= 58.6855 * 7.5
= 440.139375 cubic inches
Therefore, the volume of the equilateral triangle with an area of 6 square inches and a height of 15 inches is approximately 440.14 cubic inches.