Use the image to answer the 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.
(1 point)
Responses
952 cm3
952 cm cubed
154 cm3
154 cm cubed
448 cm3
448 cm cubed
616 cm3
616 cm cubed
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page 12 of 12
To find the volume of the composite figure, we first calculate 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 calculate the volume of one of the triangular prisms:
Volume = 0.5 x base x height x length
Volume = 0.5 x 5 cm x 4 cm x 6 cm
Volume = 60 cm3
Since there are two identical triangular prisms attached to the rectangular prism, we multiply the volume of one triangular prism by 2:
2 x 60 cm3 = 120 cm3
Finally, we add the volume of the rectangular prism to the total volume of the two triangular prisms:
280 cm3 + 120 cm3 = 400 cm3
Therefore, the volume of the composite figure is 400 cm3.
So, the correct answer is not included in the given options.