How to calculate the volume of a triangular prism

How to calculate the volume of a triangular prism
How to calculate the volume of a triangular prism
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A right triangular prism is a solid (polyhedron) that one does not meet frequently, neither in mathematics nor in everyday life. But you never know! Someday you may need to calculate the volume Vp { displaystyle V_ {p}}

{displaystyle V_{p}}

d'un tel objet. Rien de bien compliqué à cela, puisqu'il suffit de multiplier l'aire Ab{displaystyle A_{b}}

A_{b}

d'une de ses bases triangulaires par sa hauteur h{displaystyle h}

{displaystyle h}

: Vp=Ab×h{displaystyle V_{p}=A_{b}\times h}

{displaystyle V_{p}=A_{b}\times h}

Étapes

Partie 1 sur 2: Calculer l'aire d'une base triangulaire

Calculate the Volume of a Triangular Prism Step 1

Step 1. Determine the base and height

To obtain the area of ​​the triangle of a prism, you need to know the length of one of its bases and that of the associated height. These two measurements will be given in a school exercise, otherwise you will measure them on a diagram. Take the example of a prism with a base of 8 cm and a height of the base of 9 cm.

  • This is the height of the triangle, not that of the prism.
  • No matter which triangular base you choose, they are both identical.
Calculate the Volume of a Triangular Prism Step 2

Step 2. Learn and remember the formula for the area of ​​a triangle

It is quite simple and logical, since it consists of multiplying the base by its height, then dividing by 2. The formula for calculating the area of ​​a triangle is therefore as follows:

  • Ab = bh2 { displaystyle A_ {b} = { frac {bh} {2}}}

    {displaystyle A_{b}={frac {bh}{2}}}

    , Ab{displaystyle A_{b}}

    A_{b}

    étant l'aire de la base triangulaire, b{displaystyle b}

    b

    la longueur de sa base et h{displaystyle h}

    h

    sa hauteur. Cette formule se présente aussi sous la forme: Ab=12bh{displaystyle A_{b}={frac {1}{2}}bh}

    {displaystyle A_{b}={frac {1}{2}}bh}
Calculate the Volume of a Triangular Prism Step 3

Step 3. Calculate the area of ​​the triangle

To find the area of ​​the triangular base of a prism, multiply its base by its height, then divide the result by 2. The area obtained is expressed in square units, such as cm2.

  • The triangle taken as an example therefore has a base of 8 cm and a height of 9 cm. Its area is calculated as follows: Ab = 8 × 92 = 36 { displaystyle A_ {b} = { frac {8 \ times 9} {2}} = 36}

    {displaystyle A_{b}={frac {8\times 9}{2}}=36}

    . Ce triangle a donc une aire de 36 cm2.

Partie 2 sur 2: Calculer le volume du prisme

Calculate the Volume of a Triangular Prism Step 4

Step 1. Learn the formula for the volume of a right triangular prism

This volume is in fact nothing other than the stacking of the triangular base over the entire height of the prism. The formula is therefore easy to remember, since it looks like this: Vp = Ab × h { displaystyle V_ {p} = A_ {b} times h}

{displaystyle V_{p}=A_{b}\times h}

, Vp{displaystyle V_{p}}

{displaystyle V_{p}}

étant le volume du prisme, Ab{displaystyle A_{b}}

{displaystyle A_{b}}

l'aire de la base triangulaire et h{displaystyle h}

h

sa hauteur.

  • Si nous reprenons notre exemple, le calcul du volume s'écrit ainsi:

    Vp=36×h{displaystyle V_{p}=36\times h}

    {displaystyle V_{p}=36\times h}
Calculate the Volume of a Triangular Prism Step 5

Step 2. Measure the height h { displaystyle h}

h

du prisme.

Elle vous sera peut-être donnée dans un exercice, sinon mesurez-la. C'est la distance entre les deux faces triangulaires, le long d'une de ses arêtes. Nous posons que notre prisme de démonstration a une hauteur de 16 cm, valeur que vous allez mettre dans la formule.

  • Un prisme droit triangulaire de 8 cm de base, de 9 cm de hauteur de base et d'une hauteur de 16 cm a le volume suivant: Vp=36×16{displaystyle V_{p}=36\times 16}
  • {displaystyle V_{p}=36\times 16}
Calculate the Volume of a Triangular Prism Step 6

Step 3. Calculate the volume of the prism

Here is ! You are almost done! The digital application is done, all that remains is to do the calculations by multiplying the height of the prism by the area of ​​its triangular base. The result obtained will be expressed in cubic units.

  • In our example, with the units, this gives:

    V = 36 cm2 × 16 cm = 576 cm3 { displaystyle V = 36 \ cm ^ {2} times 16 \ cm = 576 \ cm ^ {3}}

    {displaystyle v=36\ cm^{2}\times 16\ cm=576\ cm^{3}}

    . le prisme a donc un volume de 576 cm3.

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