Question

an archit ct de gned a ho se to be constructed as shown. 8 ft 15 ft 30 ft 18 ft triangular prism • base - height of 8 feet and base of 18 feet • height - 30 feet rectangular prism • base - length of 30 feet and width of 18 feet • height - 15 feet how many cubic feet of space are in the house? ft³

Explanation:

Step1: Calculate the volume of the triangular prism

The formula for the volume of a triangular prism is \(V = \frac{1}{2}bh\times l\), where \(b = 18\) ft (base of the triangle), \(h = 8\) ft (height of the triangle), and \(l = 30\) ft (length of the prism).

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Step2: Calculate the volume of the rectangular prism

The formula for the volume of a rectangular prism is \(V=l\times w\times h\), where \(l = 30\) ft, \(w = 18\) ft, and \(h = 15\) ft.

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Step3: Calculate the total volume of the house

Add the volumes of the two prisms together: \(V_{total}=V_{triangular}+V_{rectangular}\)

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Answer:

\(10260\)