Question

Please take a quick look and see if i got the right answer. I just need help on this last question!
What is the volume of a triangular prism with a height of 7 inches and a base that is an equilateral triangle with sides of 6 inches?

Answer 1

Im not sure but i got 126in^3

Answer 2

base area = \[\frac{1}{2} \sin 60 \times 6 \times 6\]
volume = base area * height
i got 15.58 * 7 =109.2 inch....ur wrng :(

Answer 3

Oh well that;s not one of my answer though ;/.
The answer are...


147 in3
84sqrt3 in3
126 in3
63sqrt3 in3

Answer 4

well then thers sumthng wrng in the question

Answer 5

ok one sec

Answer 6

The formula for finding the area of a pyramid is V=1/3BH
So first we have to do the thing where you find the total for the base but idk how to do it when it says a base that is an equilateral triangle with sides of 6 inches?

Answer 7

After you find the total perimeter of the base then you input the numbers into the formula. I never saw anything about sin beign needed into this problem

Answer 8

haha is it a pyramid or a triangular prism ?

Answer 9

triangle so i made a mistake by saying V=1/3bh instead of V=1/2bh

Answer 10

not quite
Area of triangle = 1/2bh
Volume = Area of triangle * height of prism

Answer 11

yeah i meant it's a triangular prism

Answer 12

thushananth did it correctly, but just didn't leave it in terms of sqrt3

Answer 13

Oh ok so how do we do that?

Answer 14

its 63sqrt3

Answer 15

oh ok thanks but if it's no trouble can you show me how to work this out?

Answer 16

if you know trig then sin(60) = h/6 --> h = 6*sqrt3/2 = 3*sqrt3
if you don't know trig then use pythagorean thm
h = sqrt(6^2 - 3^2) = sqrt(36-9) = sqrt(27) = 3*sqrt3

Area triangle = 1/2 *6 * 3sqrt3 = 9sqrt3

Volume = 9sqrt3 * 7 = 63sqrt3