What is the volume of a right triangular prism whose height is 6 cm and its base on a equilateral tr...........

Quantitative Aptitude (CGL) Coordinate Geometry

What is the volume of a right triangular prism whose height is 6 cm and its base on a equilateral triangle which has a side of 4 cm?

11.25

67.50

41.56

33.75

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Explanation:

Splitting one side of the base triangle into two equal parts, we can use our old friend Pythagoras to calculate the length of the blue line, which is the height of the triangle.
42=22+x2→x2=16−4=12→x=√12=√23
Now, the area of a triangle is simply half its base multiplied by its height, so:
Area=√4223=43
Volume=Area×prism height=√43×6=√243
≈41.5692193817
Answer (rounded to 3 decimal places) 41.56 cm3