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A triangular prism has a volume of 2040 units3. The dimensions of the base of the prism is 20, the left side is 12 and the hypotenuse is 16




What is the height of the prism?



96 units



6.76 units



21.25 units



10.63 units

Respuesta :

wolf1728
20 * 12 * 16 * height = 2,040
height = 2,040 / (20 * 12 * 16)
height = 2,040 / 3,840
height = 0.53125
Is that problem written correctly?

Answer:

The answer is C

Step-by-step explanation:

The volume of a prism is = Area of Base * Height

Area of Base: Since this is a scalene triangle, we use herons formula for area = SQRT[s (s-a)(s-b)(s-c)], where s is the semi perimeter = (a+b+c)/2 = (12+16+20)/2 = 24

Therefore Area = Sqrt[ 24 (24-12)(24-16)(24-20)] = Sqrt (24*12*8*4) = Sqrt(9216) = 96

Therefore Volume = 2040 = 96 * h

or h = 2040/96 = 21.25 units (Option 3)

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