Question

What is the volume of a triangular prism with a height of 3 centimeters and a base that is an equilateral triangle with sides of 4 centimeters?

24 cm3

8*sqrt*(3) cm3

12*sqrt*(3) cm3

48 cm3

Answer 1

I believe that you have to find the area of the triangle..let that be E.
To do that you get the formula \[E = (base * height ) / 2 \]
In your case what is the hight of the equilateral triangle?

You may find it using the Pythagorean theorem, let the height be h1
\[h ^{2} = 4^{2} + 4 ^{2} => h = \sqrt{32}\]

So what we get is this:
\[E = 4 * \sqrt{32} / 2 = 2 * \sqrt{32}\] square cm

To get the volume, let that be V, you get this:
\[V = E * height\]
Height in your case is 3 cm.

So \[V = 2 * \sqrt{32} * 3 = 6* \sqrt{32}\]


I hope I am correct..

Answer 2

Take a look at the drawing. Since equilateral triangles are isosceles, if we draw the altitude, then it bisects the base (and the angle). So, we can split the base into two right triangles with a hypotenuse of 4 and a leg of 2.

Do you know about 30-60-90 triangles? The sides opposite the respective angles are in the ratio 1: sqrt 3 : 2. So, looking at our picture, the height of our equilateral triangle is 2 sqrt 3.

The area of a triangle is bh/2. Plugging everything in, the area of this equilateral triangle is 2 sqrt 3 * 4 / 2. This evaluates to 4 sqrt 3.

The area of a prism is Bh, where B is the area of the base. Well, we just calculated that, so all we need to do is plug it in.

A prism = 4 sqrt 3 * 3 = 12 sqrt 3

Answer 3

Aww man! Forgot to insert picture. I always do that...

Don't forget units: cm cubed.