A triangular prism has a volume of 2040 units3 The dimension

A triangular prism has a volume of 2040 units3. The dimensions of the base of the prism are shown below. 12 16 20 y Question Completion Status What is the height of the prism? O 96 units O 6.76 units O 21.25 units 10.63 units

Solution

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)