Question

the base of a right prism is an equilateral triangle each of whose sides measures 4cm.the altitude of the prism measures 5cm.Find the volume of the prism ​

Answer 1

To find the volume of the prism, you need to calculate the area of the equilateral triangle base and then multiply it by the altitude of the prism.

Step-by-step explanation:

To find the volume of the prism, we first need to calculate the area of the base. Since the base is an equilateral triangle, we can use the formula A = (√(3)/4) × s², where A is the area and s is the length of one side of the triangle.

In this case, s = 4cm. So, the area of the base is A = (1.732/4) × 4² = 6.928 cm².

Next, we can calculate the volume of the prism using the formula V = A × h, where V is the volume, A is the area of the base, and h is the altitude of the prism. In this case, h = 5cm.

So, the volume of the prism is V = 6.928 cm² × 5cm = 34.64 cm³.

Answer 2

`V=34.64\ cm^3`

Step-by-step explanation:

Given that,

The side of an equilateral prism = 4 cm

The altitude of the prism = 5 cm

We need to find the volume of the prism. The formula for the volume of a prism is as follows :

`V=A* h`

Where

A is the area of equilateral triangle,
`A=(\sqrt3)/(4)a^2`

So,

`V=(\sqrt3)/(4)a^2* h\\\\V=(\sqrt3)/(4)* 4^2* 5\\\\V=34.64\ cm^3`

So, the volume of the prism is equal to
`34.64\ cm^3`.