Question

Can someone help me with this

Answer 1

Answer:

  A) 24 ft³

Step-by-step explanation:

The area of the right triangle base is ...

  A = (1/2)(3)(4) = 6 ft²

The volume of the triangular prism is the product of the area of its base (6 ft²) and its height (4 ft).

  V = Bh = (6 ft²)(4 ft) = 24 ft³ . . . . matches choice A

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Comment on the triangle

You know the 3-4-5 triangle is a right triangle, because you have seen those numbers many times in relation to the Pythagorean theorem. If you don't know that, then you can check to see by using the Pythagorean theorem:

  5² = 3² +4²

  25 = 9 + 16 . . . . . true; so the triangle is a right triangle

In any event, there are other means for finding the area of the triangle based on the lengths of its sides. You will get the same area result.

Using Heron's formula, s = (a+b+c)/2 = (3+4+5)/2 = 6.

  A = √(s(s -a)(s -b)(s -c)) = √(6(3)(2)(1)) = √36 = 6 . . . . area of base triangle