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)
To find the total volume of the dollhouse, we need to calculate the volume of the rectangular prism and the volume of the two triangular prisms, then add them together.
Volume of rectangular prism = length x width x height
= 8 x 10 x 12 = 960 cubic inches
Volume of one triangular prism = 1/2 x base x height x perpendicular height
= 1/2 x 8 x 6 x 12 = 288 cubic inches
(total volume from both triangular prisms = 2 x 288 = 576 cubic inches)
Total volume = volume of rectangular prism + total volume of two triangular prisms
= 960 + 576
= 1536 cubic inches
Therefore, the total volume of the dollhouse is 1536 cubic inches.