Question

Find an expression for the volume of a triangular prism is a right triangle with bade 4x 6 and height x 5 and the height triangular prism is x 5 Use the expression to find the volume hen x=3

Answer 1

The volume of a triangular prism can be found using the formula: V = (base area) x height. For a right triangle with base 4x6 and height x5, the base area is (1/2) x (4x6) = 12x. The height of the prism is x5. Therefore, the volume expression is V = 12x * x5 = 60x^2. To find the volume when x = 3, substitute x = 3 into the expression: V = 60(3^2) = 540. Therefore, the volume of the triangular prism when x = 3 is 540 units^3.

Answer 2

To find the expression for the volume of a triangular prism, we need to know the formula for the volume of a prism. The formula for the volume of any prism is given by:

Volume = Base Area * Height

In this case, the triangular prism has a right triangle as its base, with base length 4x and height 6, and the height of the prism is x 5.

Step 1: Find the area of the base triangle

The area of a triangle is given by the formula: Area = (1/2) * base * height. In this case, the base length is 4x and the height is 6. Therefore, the area of the base triangle is:

Base Area = (1/2) * (4x) * 6 = 12x

Step 2: Calculate the volume

Now that we have the base area and the height of the prism, we can calculate the volume using the formula:

Volume = Base Area * Height

Substituting the values we have:

Volume = 12x * (x 5)

Simplifying the expression:

Volume = 12x^2 + 60x

To find the volume when x = 3, we can substitute x = 3 into the expression:

Volume = 12(3)^2 + 60(3)

= 12(9) + 180

= 108 + 180

= 288

Therefore, when x = 3, the volume of the triangular prism is 288 units cubed.