Question

2. The base of a triangular prism is an equilateral triangle with sides 24 mm long.The height of the prism is 7 mm. Find the volume of the prism. (3pts)24 mm24 mmI24 mm

Answer 1

The volume of a prism can be calculated by multiplying the area of its base by its height. The height is given, so we need the area of the base.

`V=A\cdot h_p`

The base is an equilateral triangle with side, s, with length 24 mm. To find the area of the triangle, we need the base, which is the either side, and the height of the triangle. The heigh of an equilateral triangle is:

`h_t=\frac{s\sqrt[]{3}}{2}=\frac{24\sqrt[]{3}}{2}=12\sqrt[]{3}`

So, the area of the triangle is:

`A=(s\cdot h_t)/(2)=\frac{24\cdot12\sqrt[]{3}}{2}=12\cdot12\sqrt[]{3}=144\sqrt[]{3}`

So, the volume of the prims is:

`V=A\cdot h_p=144\sqrt[]{3}\cdot7=1008\sqrt[]{3}\approx1746`

So, the volum of the prims is 1746 mm³.