Question

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

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve for the volume of the composite figure, we first need to find the volume of each individual prism and then add them up.

Volume of rectangular prism:
length x width x height
= 14 cm x 5 cm x 4 cm
= 280 cm³

Volume of each triangular prism:
1/2 x base x height x length
= 1/2 x 5 cm x 6 cm x 14 cm
= 210 cm³ (for each triangular prism)

Since there are two identical triangular prisms, we need to multiply the volume of one prism by 2 to account for both:
2 x 210 cm³ = 420 cm³

Now, to find the total volume of the composite figure, we add the volume of the rectangular prism and the two triangular prisms together:
280 cm³ + 420 cm³ = 700 cm³

Therefore, the volume of the composite figure is 700 cm³.