Pyramid Volume

dmg24

Hi guys,

I am having a major blonde moment. I'm trying to work out the area of a pyramid with a triangular base, and I keep getting different answers!

The base has sides of 2.62 cm, and the three sides leading to the apex are each 1.85 cm.

For the base calculation I am doing (2.62 x 2.62 x 1/2) = 3.4322, but then I keep changing my mind on the height.

Any help gratefully received! x

Chall

I make it 3.4322 for the base, 1.306292 for the height, and therefore 4.483457 for the volume, so 4.48cm^3 correct to 3 s.f.

dmg24

Thanks Chall,

That's what I got first time (maybe I should have more faith in myself?!). But then I keep changing my mind.

Edit: But I got 4.48 x 1/3 for the volume. Is that what you meant?!

mug51

i got the height to be 1.46

mug51

maybes i am wrong

then do watever you do to find the volume base*height*1/3

Blacksheep1979

yeah I agree with mug - I think you have the area of the base wrong as its 1/2 base times hight not half side times side.

dmg24

There are two of us sat here and A has the first answer, and I have the second.

Anyone want the deciding vote?!

Blacksheep1979

ok the area of the base is ((1.31tan60) * 2.62) / 2

the triangle that makes up a verticle from the tip of the pyramid to the base and out to the corner is 1.85 hypotenuse and the distance from the corner to the point directly under the top of the pyramid is equidistant from every base corner. So that length is

1.31 / (cos 30)

from there you have two sides of the triangle that makes up the hypotenuse on the pyramid and the base length . from that you can get the angle as

inverse cos ((1.31 / (cos 30)) / 1.85)

then sin of that angle and the hypotenuse will give you the height of the pyramid or use pythagorus

so 1.85 * sin(inverse cos ((1.31 / (cos 30)) / 1.85))

1/3 times ^ times area of base is your answer.

Blacksheep1979

so I get 1.446 for the volume

dmg24

Thank you all so much ... you are superstars!

I finally got the answer to 1.446 also.

The next round is on me x

Chall

I can't even remember if what I used to get the area of a square based pyramid was right, plus I don't have a calculator and haven't done that sort of maths in over a year, but I don't see why you followed so many trigonometric functions when to work out the height pythagorus theorem would have done