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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

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 676 units 2125 un class=

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TaeKwonDoIsDead

Answer:

Height = 21.25 units

Step-by-step 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:

[tex]A=\sqrt{p(p-a)(p-b)(p-c)}[/tex]

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,

[tex]A=\sqrt{p(p-a)(p-b)(p-c)}\\A=\sqrt{24(24-20)(24-16)(24-12)}\\A=\sqrt{(24)(4)(8)(12)} \\A=\sqrt{9216} \\A=96[/tex]

Thus,

Volume = 96 * height

2040 = 96 * height

height = 2040/96 = 21.25 units

Answer:

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)