Question

A triangular prism has a volume of 2040 units. The dimensions of the base of the prism are shown below.

What is the height of the prism?
96 units
6.76 units
21.25 units
10.63 units

Answer 1

The answer is C

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)

Answer 2

Height = 21.25 units

Explanation:

Triangular prism (with triangular base at bottom) will have volume formula as:

Triangular Prism Volume = area of base * height

We need to find area of base (which is the triangle shown).

We can use heron's formula which is:

`A=√(p(p-a)(p-b)(p-c))`

Where

A is area

p is HALF of the perimeter (sum of all sides)

a,b,c are the three sides

So p = (12+16+20)/2=24

Now,

`A=√(p(p-a)(p-b)(p-c))\\A=√(24(24-20)(24-16)(24-12))\\A=√((24)(4)(8)(12)) \\A=√(9216) \\A=96`

Thus,

Volume = 96 * height

2040 = 96 * height

height = 2040/96 = 21.25 units