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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?
Wiki User
∙ 8y ago
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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
Wiki User
∙ 8y ago
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