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# Volume of triangular pyramid

So, I have a triangular based pyramid made of 3 congruent isosceles triangles, they are 9 cm by 11 cm by 9 cm, and it's 45 degree angles. What is the volume and formula?

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Here is to get you started. To increase the size of the image do a CTRL Plus (+) in your browser.
You need to calculate the slant height of the pyramid for the formula of the lateral area. You should find a value of (1/2)*SQRT(203) or about 7.1239 cm

You need to calculate the altitude (height) of the pyramid from the apex (summit) to the center of the base triangle (center of inscribed circle, barycenter, orthocenter). The hypotenuse of such triangle is the slant height. One leg is the altitude (to be found), the measure of the second leg is (1/3) the altitude of the equilateral triangle that forms the base. You should find (1/3) m MH= (1/3)* (11/2)*SQRT(3)

1. Calculate the area of the base (use a formula for the equilateral triangle or the general formula for a triangle: you have its height MH ).
2. Lateral area = 3 times the area of triangle Triangle ECD (in yellow above).
3. Total area = area of base + lateral area.
4. Volume= (1/3)(Area of base)* (height of pyramid)
If you can see the details on the screen capture below, fine, Press CTRL + in your browser to increase the size.

Posted on Mar 30, 2014

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Posted on Jan 02, 2017

might try

(54tan)/45

I don't have a calc that will do it or I would try it and see.

Posted on Aug 01, 2008

Hi - welcome to Fixya.

You're refering to Trigonometry or 'Trig'. The basic formula is easily remembered as SOH-CAH-TOA:

SOH: Sine of an angle is Opposite over Hypotenuse **
CAH: Cosine of an angle is Adjacent over Hypotenuse **
TOA: Tangent of an angle is Opposite over Adjacent **

** See attached image below

I can't tell you which buttons to press on your calculator, but you can download a new manual from here:

http://www.retrevo.com/support/TI-TI-30Xa-Calculators-manual/id/421ci270/t/2/

If you have any trouble downloading the instruction manual or you have any further maths questions, please post back and I will be happy to assist you.

Regards,
BElectric.

Posted on Nov 23, 2010

When you have to deal with problems of this sort, you usually are given recipes or mathematical formulas which you apply to find the result. It so happens that for the volumes of cylinders, the formula to use is
Volume = Area of the base times the height=Ab*h
If the cylinder is circular, then the area of the base is that of a disk, Ab=PI*r^2`where r is the radius.
In your case, you are given the diameter (twice the radius) and the height.
Volume =PI*h*(6.2/2)^2, the unit being cm^2

To type in the value of PI, press [2nd] [^] (the latter is key under CLEAR, and above the division sign.
To raise a number to power 2 (to square it), use the key marked x with a superscript 2, or x with a raised 2.
After you have typed in all necessary ingredients in the formula, press the [ENTER] key and the calculator will give you the result.

Now, it is your turn to do some mathematics.

Posted on Jun 16, 2011

Yes, there is shortcut because this is right triangle, so you can use Pythagorean theorem (see picture).

1. Length of hypotenuse is square root of sum of squares of lengths of other two sides of triangle, which is equal to square root of 30^2+10^2=31.6 cm.
2. Sin(a)=longer cathetus/hypotenuse=0.949 so a=arcsin(0.949)=71.6 degrees
3. Finally b=90-a=18.4 degrees.

If this was helpful please rate 4 thumbs :)

Posted on Sep 05, 2011

About 146 and a half degrees.

If this is homework, make sure to show your work.

Posted on Oct 22, 2013

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