What is the volume formula of trapezoid

What is the volume of prisms?

Since prisms are solids, they can be filled.

If you fill a prism with water and measure this in a measuring cup, you will get the volume of the prism. The volume tells you how much liquid fits into a prism.

You can also fill prisms with unit cubes. The volume of the prism then indicates how many unit cubes fit into the prism.

In the case of prisms with "pointed" corners, the layout with the unit cubes is no longer so good.

But you can use a formula that fits all straight bodies: base area $$ * $$ height

How to calculate the volume of a prism:

  1. Calculate the base area.
  2. Calculate the volume. Volume $$ = $$ base area $$ * $$ body height. Short notation: $$ V = G * h_k $$

A Unit cube has the edge length $$ a = 1 $$ $$ cm $$ and thus the volume $$ V = 1 $$ $$ cm ^ 3 $$.

The volume is given in $$ cm ^ 3 $$ (read: cubic centimeters).

Let's go: the triangular prism

A triangular prism with the edge lengths is given

$$ a = 4 $$ $$ cm $$,
$$ b = h_a = 3 $$ $$ cm $$,
$$ h_k = 2 $$ $$ cm $$.

To calculate the volume, do the following:

1. Calculate the base area.

The base is a right triangle.

$$ G = 1/2 g * h $$ (any triangle)

$$ G = 1/2 a * b $$ (right triangle)

$$ G = 1/2 4 $$ $$ cm * 3 $$ $$ cm $$

$$ G = 1/2 12 $$ $$ cm ^ 2 $$

$$ G = 6 $$ $$ cm ^ 2 $$

For the basic page $$ g $$ you use the side $$ a $$, for $$ h $$ the side $$ b $$. Since it is a right-angled triangle, the $$ b $$ side is also at the same time the triangular height $$ h_a $$ to the $$ a $$ side (at a right angle to it).


2. Calculate the volume.

Volume $$ = $$ base area $$ * $$ body height

$$ V = G * h_k $$

$$ V = 6 $$ $$ cm ^ 2 * 2 $$ $$ cm $$

$$ V = 12 $$ $$ cm ^ 3 $$

$$ h_a $$ denotes the height of the triangle side $$ a $$.

Area of ​​a triangle: $$ G = 1/2 g * h $$

  • $$ g $$ basic page
  • $$ h $$ Height of the triangle
Tip:

The height of the base is not the height of the body $$ h_k $$.

Calculate the volume of any prism

Prisms can have different bases.

Depending on which prism it is, use other formulas to calculate the base area $$ G $$.

Base of the prismUse the following formulas:
triangle
$$ G = 1/2 g * h $$
parallelogram

$$ G = a * h_a $$
Trapezoid

$$ G = (a + c) / 2 * h $$


Then you always do the math:
Volume $$ = $$ base area $$ * $$ body height

Base of the prismUse the following formulas:
square

$$ V = a ^ 3 $$
rectangle

$$ V = a * b * c $$

$$ V = G * h_k $$


The Body height $$ h_k $$ is the route that connects the two areas: