Find the volume of the triangular prism described below.

Question

The base is a 45degrees​)-45degrees)​-90degrees triangle with a leg of 5 in. The height is 1.2 in.
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Part 1
The volume of the prism is
  

Answer 1

equal to the area of the base triangle multiplied by the height of the prism.

First, we need to find the area of the base triangle. Since it is a 45-45-90 triangle with one leg of 5 inches, we can find the length of the other leg using the Pythagorean theorem:

a^2 + b^2 = c^2
5^2 + 5^2 = c^2
25 + 25 = c^2
50 = c^2
c = sqrt(50) = 5√2

Now, the area of the triangle is:
Area = 1/2 * base * height
Area = 1/2 * 5 * 5√2
Area = 12.5√2 square inches

Next, we multiply the area of the base triangle by the height of the prism to get the volume:
Volume = Area of base * height
Volume = 12.5√2 * 1.2
Volume ≈ 15.00 cubic inches

Therefore, the volume of the triangular prism is approximately 15.00 cubic inches.

Answer 2

no, the hypotenuse is 5√2. The other leg is also just 5.
So the area of the triangle is 25/2

Answer 3

You are correct, I apologize for the error. The base triangle is a 45-45-90 triangle with legs of length 5 inches.

The area of a triangle is given by the formula:
Area = 1/2 * base * height

For the base triangle:
Base = 5 in
Height = 5 in

Area = 1/2 * 5 * 5 = 25/2 = 12.5 square inches

Now, to find the volume of the triangular prism, we multiply the area of the base by the height of the prism:
Volume = Area of base * height
Volume = 12.5 * 1.2
Volume = 15

Therefore, the volume of the triangular prism is 15 cubic inches. Thank you for catching that mistake.