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
154 cm3
154 cm cubed
952 cm3
952 cm cubed
448 cm3
448 cm cubed
616 cm3
To solve for the volume of the composite figure, we first need to find the volume of the rectangular prism and the volume of the two triangular prisms.
Volume of rectangular prism = length x width x height
Volume of rectangular prism = 14 cm x 5 cm x 4 cm
Volume of rectangular prism = 280 cm^3
Volume of two triangular prisms = 2 x (1/2 x base x height x length)
Volume of two triangular prisms = 2 x (1/2 x 5 cm x 6 cm x 4 cm)
Volume of two triangular prisms = 2 x (60 cm^3)
Volume of two triangular prisms = 120 cm^3
Total volume of composite figure = Volume of rectangular prism + Volume of two triangular prisms
Total volume of composite figure = 280 cm^3 + 120 cm^3
Total volume of composite figure = 400 cm^3
Therefore, the volume of the composite figure is 400 cm^3.