Question

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

Answer 1

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:

$A=\sqrt{p(p-a)(p-b)(p-c)}$

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,

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

Thus,

Volume = 96 * height

2040 = 96 * height

height = 2040/96 = 21.25 units