Use the image to answer the question.
An illustration shows a that is shaped like a rectangular prism with two triangular prisms placed on the top, one on each side. The width of the rectangular prism is 10 inches, and the height is 12 inches. The base length of the triangular prisms on the top of the house is 8 inches each. There is a 2-inch gap between the two triangular prisms. The perpendicular height of the triangular prisms is 6 inches. A window is drawn on the face of each triangular prism, and a door is drawn on the bottom center of the rectangular prism.
Write and solve an expression for the total volume of the dollhouse.(1 point)
Responses
2,640 in.3
2,640 in. cubed
264 in.3
264 in. cubed
3,120 in.3
3,120 in. cubed
2,400 in.3
2,400 in. cubed
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To find the total volume of the dollhouse, we first find the volume of the rectangular prism, then add the volume of the two triangular prisms.
Volume of rectangular prism = length x width x height
Volume of rectangular prism = 8in x 10in x 12in = 960 in^3
Volume of each triangular prism = 1/2 x base x height x length
Volume of each triangular prism = 1/2 x 8in x 6in x 8in = 192 in^3
Total volume = 960 in^3 (rectangular prism) + 2(192 in^3) (two triangular prisms)
Total volume = 960 in^3 + 384 in^3 = 1,344 in^3
So, the total volume of the dollhouse is 1,344 in^3.
None of the given options match the correct answer of 1,344 in^3.