Answer:
14 inches^3
Explanation:
Volume formula for a triangular pyramid:
V = 1/3BH
Where "B" represents the base (meaning the full area of the base of the triangular pyramid) and "H" represents the height (the dotted line that runs through the entire pyramid).
We are given:
Width of base = 3 inches
Length of base = 4 inches
Height of pyramid = 7 inches
Let's first find the area of the base using the formula for the area of a triangle:
A = 1/2BH
(the "B" in this case would represent the width and the "H" would represent the length, so just use those values for this),
Substitute:
A = 1/2(3)(4)
Solve:
A = 1/2(12)
A = 12/2
A = 6
Now we know that the base of the triangular pyramid is 6, let's plug this into the volume formula:
V = 1/3BH
(Remember! The base we found is 6, so we use that for the "B" in this formula), also the height of this pyramid is 7 inches:
V = 1/3(6)(7)
V = 1/3(42)
V = 42/3
V = 14 inches^3 is the volume of this pyramid.
Where you might have gone wrong:
I think your mistake was that you used the wrong volume formula for this figure. You might have used the triangular prism volume formula, however, in this situation, you weren't supposed to use it because the base of one side is a triangle but not the other.
The formula you probably used:
V = 1/2BHL
Where "B" represented the shorter side of the base(basically the width of the base) of the pyramid, "H" represented the height of the pyramid, and "L" represented the longer side of the base of the pyramid.
So, I'm sure you carried out this execution:
V = 1/3BHL
V = 1/3(3)(7)(4)
V = 1/3(21)(4)
V = 1/3(84)
V = 84/3
V = 28, this is wrong.
Hope this helps! :)