What is the volume of this triangular prism?

Mathematics

2 answers:

LuckyWell [14K]3 years ago

6 0

Answer:

$V=5,676.16\ cm^{3}$

Step-by-step explanation:

we know that

The volume of the triangular prism is equal to

$V=BL$

where

B is the area of the triangular face

L is the length of the triangular prism

Find the area of the triangular face B

$B=\frac{1}{2}(28*22.4)= 313.6\ cm^{2}$

we have

$L=18.1\ cm$

substitute the values

$V=313.6*18.1=5,676.16\ cm^{3}$

Liula [17]3 years ago

4 0

Answer:

5676.16 cm^3

Step-by-step explanation:

The volume of any prism is given by the formula ...

V = Bh

where B is the area of one of the parallel bases and h is the perpendicular distance between them. Here, the base is a triangle, so its area will be ...

B = 1/2·bh

where the b and h in this formula are the base and height of the triangle, 28 cm and 22.4 cm.

Then the volume is ...

V = (1/2·(28 cm)(22.4 cm))·(18.1 cm) = 5676.16 cm^3

_____

You will note that this is half the product of the three dimensions, so is half the volume of a cuboid with those dimensions. Perhaps you can see that if you took another such prism and placed the faces having the largest area against each other, you would have a cuboid of the dimensions shown.

You might be interested in

Using a linear approximation, estimate f(2.1), given that f(2) = 5 and f'(x) = √3x-1.

algol [13]

Answer:

$f\left( {2.1} \right) \approx 5.22360$ .

Step-by-step explanation:

The linear approximation is given by the equation

${f\left( x \right) \approx L\left( x \right) }={ f\left( a \right) + f^\prime\left( a \right)\left( {x - a} \right).}$

Linear approximation is a good way to approximate values of $f(x)$ as long as you stay close to the point $x= a$ , but the farther you get from $x=a$ , the worse your approximation.