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?
Answer

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?
 Answer

anonymous · Answer

wot u think ?

anonymous · Answer

These were the choices:
 24cm cubed
12*sqrt*3cm cubed
48 cm cubed 
8*sqrt*3 cm cubed

campbell_st · Answer

The formula is

$$V=\frac{1}{3} Base Area \times height$$

For the triangular base

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find the height of the equilateral triangle by 
using Pythagoras' thorem

h^2 = 4^2 - 2^2

$$h = \sqrt{12}$$

$$h = 2\sqrt{3}$$

BAse Area  the triangle is 

$$A = 1/2\times 4 \times2 \sqrt{3} = 4\sqrt{3}$$

Volume is 

$$V = \frac{1}{3} \times 4\sqrt{3} \times3$$

campbell_st · Answer

ooop... thought it said pyramid

but here is the prism information 

Volume = cross section area x length

$$V = 4\sqrt{3} \times 3 = 12\sqrt{3}$$

anonymous · Answer

thank you