Use the image to answer the question.

Question

An illustration shows a rectangular prism joined two triangular prisms on either side. The illustration shows two identical triangular prisms, each with one side attached to the length of the rectangular prism. The sides attached to the rectangular prism are oriented such that the triangular prisms are mirror images of one another. The length of the rectangular prism is 14 centimeters. The width and the height are 5 centimeters and 4 centimeters respectively. The distance from the apex of the triangular prism to the base is 6 centimeters.

Solve for the volume of the composite figure.
154 cm3
448 cm3
616 cm3
952 cm3

Answer 1

First, we need to find the volume of the rectangular prism:

Volume = Length x Width x Height
Volume = 14 cm x 5 cm x 4 cm
Volume = 280 cm3

Next, we need to find the volume of one triangular prism and then multiply it by 2 since there are two identical triangular prisms.

Volume of one triangular prism = (1/2) x base x height x length
Volume of one triangular prism = (1/2) x 5 cm x 6 cm x 4 cm
Volume of one triangular prism = 60 cm3

Total volume of both triangular prisms = 60 cm3 x 2 = 120 cm3

Finally, we add the volume of the rectangular prism and the volume of the two triangular prisms to get the total volume of the composite figure:

Total volume = Volume of rectangular prism + Volume of triangular prisms
Total volume = 280 cm3 + 120 cm3
Total volume = 400 cm3

Therefore, the volume of the composite figure is 400 cm3.