Question

ed is making a model of a square pyramid for his world history class. the model pyramid is attached to a platform, shown below. he plans to cover the entire surface of the combined model and platform with paper mache, including the bottom. what is the total surface area ed plans to cover in paper mache? square inches

Explanation:

Step1: Calculate the surface area of the square pyramid

The base of the pyramid is a square with side length \(a = 7\) inches. The area of the base \(B=a^{2}=7^{2}=49\) square inches.
The lateral surface area of a square pyramid: The formula for the lateral surface area of a square pyramid is \(LSA = 2al\), where \(a\) is the base side - length and \(l\) is the slant height. Here \(a = 7\) inches and \(l=6\) inches. So \(LSA=2\times7\times6 = 84\) square inches.

Step2: Calculate the surface area of the rectangular prism (platform)

The formula for the surface area of a rectangular prism is \(SA=2(lw + lh+wh)\). But since the base of the prism is attached to the pyramid, we need to adjust. The dimensions of the prism: \(l = 7\), \(w = 7\), \(h = 2\).
The surface area of the prism part: The area of the top of the prism is covered by the base of the pyramid. So the surface - area of the prism \(S_{prism}=2\times(7\times2 + 7\times2)+7\times7\)

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Step3: Calculate the total surface area

The total surface area \(A\) is the sum of the lateral surface area of the pyramid and the surface area of the prism.
\(A=84 + 105=189\)

Answer:

189