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What is the volume of an equilateral triangular prism whose height is the square root of 12 cm and has a length of 4 cm showing work?
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To help you, the prism will have a triangular base where the triangle is an equilateral triangle (all edges are the same length)
The interior angles of an equilateral triangle are all 60 degrees.
The square root of 12cm is 3.46 cm
the length of the prism is 4 cm
To work out the answer
(1) work out the area of the triangle - you will need to bisect one angle to make 2 identical right angle triangles inside the bigger equilateral triangle. This bisecting line will be 3.46 cm and the triangles will have internal angles of 90, 60 and 30 degrees. Using this information and Pythagoras' theorem you will be able to work out the length of a side of the equilateral triangle.
Once you have this length, the area of an equilateral triangle is provided by the formula.
Area = sqrt(3)/4 a2 (where "a" is the length of a side)
(2) multiply this by the length.
Further Information:
Using trigonometry each side of the triangle: square root of 12/sin(60 degrees)=4 cm
Volume: 0.5*4*4*sin(60 degrees)*4=27.713 cubic cm rounded up to 3 decimal places
What else can I help you with?
What is the area of a triangular prism if the height is W inches the length W inches and the base W inches?
The answer depends on what sort of triangle: right angled, equilateral, isosceles or scalene.
What is the base and height of an equilateral triangle with an area of 12?
The base length is 5.2643 units and the height is 4.55902 units.
How do you find length and width of a square showing only the height of the square?
the height is the same as the length and width
Height of a triangular based pyramid?
The height of a triangular based pyramid is given by h=2V/(bxl). V is its volume, b its base and l its length.
How do you calculate height of a equilateral triangle?
square root (3) * side length / 2
What is the area of a triangular prism if the height is W inches the length W inches and the base W inches?
The answer depends on what sort of triangle: right angled, equilateral, isosceles or scalene.
Volume of a triangular prism?
base*height*length*.5
What is the volume of a triangular prism?
One half base times height (of the triangular section) times length.
What is the height of an equilateral triangle with a length of x?
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.
What triangular shape has All three sides the same length and all three angles the same size?
That's an "equilateral triangle". Each inside angle is 60 degrees.
What is the base and height of an equilateral triangle with an area of 12?
The base length is 5.2643 units and the height is 4.55902 units.
How do you find length and width of a square showing only the height of the square?
the height is the same as the length and width
Height of a triangular based pyramid?
The height of a triangular based pyramid is given by h=2V/(bxl). V is its volume, b its base and l its length.
How do you calculate height of a equilateral triangle?
square root (3) * side length / 2
The formula for finding the volume of a triangular prism?
A triangular prism can be thought of as a stack of triangles. Then the volume is equal to the area of the triangular base multiplied by the height of the prism, or 1/2 length * width * height.
A triangular prism has a triangular face with a base of 13 yards and a height of 13.3 yards. Its volume is 1037.4 cubic yards. What is the length of the triangular prism?
Length of triangular prism: 1037.4/(0.5*13*13.3) = 12 yards
How can you form four equilateral triangles with six toothpicks of equal length?
Think in 3-dimensions and make a tetrahedron (a triangular pyramid).
