Answer:
1248 cm³
Explanation:
You want the volume of the triangular prism with height 16 cm. The triangular base has a base dimension of 13 cm and a height of 12 cm.
Volume
The volume of any prism is the product of the area of its base and the distance between the bases (prism height).
V = Bh . . . . . B is the base area, h is the height
Base
The triangular base of this prism is a triangle with its base measuring 13 cm and its height measuring 12 cm. The area of this triangle is ...
A = 1/2bh
A = 1/2(13 cm)(12 cm) = 78 cm²
Prism volume
Then the volume of the prism is ...
V = (78 cm²)(16 cm) = 1248 cm³
The volume of the triangular prism is 1248 cubic centimeters.
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Additional comment
The bases of the prism are the two faces that are congruent and parallel to each other. They are the triangles. The distance between them is the height (or length) of the prism.
You may have noticed that the volume of a triangular prism is 1/2 the volume of a rectangular prism with the same dimensions. (This is because the base triangle has half the area of a rectangle with the same dimensions.)
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