The volume of a triangular prism is 132 cubic inches . The height of the prism is 11 inches. What are the dimensions and base length of the triangular surface
well, the base has area 132/11 = 12
so ...
5 and 2
To find the dimensions and base length of the triangular surface, we first need to know the formula for the volume of a triangular prism.
The formula for the volume of a triangular prism is given by V = (1/2) * b * h * H, where b is the length of the base of the triangle, h is the height of the triangle, and H is the height of the prism.
In this case, we are given that the volume of the prism is 132 cubic inches and the height of the prism is 11 inches. Let's substitute these values into the formula and solve for the base length.
132 = (1/2) * b * h * 11
Divide both sides of the equation by 11:
12 = (1/2) * b * h
Now, we need additional information to determine the dimensions and base length of the triangular surface.
To find the dimensions and base length of the triangular surface, we first need to understand the formula for the volume of a triangular prism.
The formula to calculate the volume of a triangular prism is given by:
Volume = (1/2) * (Base Length) * Height * Width
In this case, we are given the volume (132 cubic inches) and the height (11 inches). We need to find the dimensions and base length of the triangular surface.
Let's break it down step by step:
Step 1: Substitute the given values into the formula
132 = (1/2) * Base Length * 11 * Width
Step 2: Simplify the equation
132 = 5.5 * Base Length * Width
Step 3: Divide both sides by 5.5
24 = Base Length * Width
Step 4: Find the possible factors of 24 that could represent the base length and width combination:
1 x 24
2 x 12
3 x 8
4 x 6
These are the possible combinations of base length and width that can result in a product of 24.
Step 5: Since the problem mentions that it is a triangular prism, the base length and width must be related to the triangular shape. A triangle has three sides, so we need one of the combinations that represents three different numbers.
From the possible combinations, we can see that 4 and 6 appear as different numbers. Therefore, the base length should be 4 inches and the width should be 6 inches.
The dimensions and base length of the triangular surface are:
Base Length = 4 inches
Width = 6 inches