Question

what is the surface area of this composite solid? use 11.3 meters for the slant height of the triangular prism. enter your answer in the box. m²

Explanation:

Step1: Calculate the area of the triangular faces

The formula for the area of a triangle is \(A = \frac{1}{2}bh\). Here, \(b = 16m\) and \(h\) (slant height) \(= 11.3m\). There are 2 triangular faces.
\(A_{triangles}=2\times\frac{1}{2}\times16\times11.3 = 16\times11.3=180.8m^{2}\)

Step2: Calculate the area of the rectangular faces of the prism

There are 3 rectangular faces. Two have dimensions \(12m\times20m\) and one has dimensions \(16m\times20m\).
\(A_{prism - rectangles}=(2\times12\times20)+(16\times20)=480 + 320=800m^{2}\)

Step3: Calculate the area of the rectangular faces of the lower part

The lower part has two faces with dimensions \(15m\times12m\) (assuming a typo and it should be \(16m\times12m\) for a proper composite solid calculation, but if we go with the given numbers in a standard way). Wait, re - evaluating:
The composite solid's surface area:
The two triangular faces (\(180.8m^{2}\)), the three lateral faces of the triangular prism (two with \(12\times20\) and one with \(16\times20\)), and the two faces of the lower rectangular part (assuming no overlapping in a proper way).
Another approach:
The surface area of the composite solid \(S\):
The two triangular faces: \(A_{1}=2\times\frac{1}{2}\times16\times11.3 = 180.8\)
The three lateral faces of the triangular part: \(A_{2}=(16 + 12+12)\times20=(40)\times20 = 800\) (using the perimeter of the base of the triangular part times the length)
We also have the two faces of the lower rectangular part (assuming no double - counting). Wait, no:
The formula for the surface area of the composite solid:
The two triangular faces (\(A_{t}=2\times\frac{1}{2}\times16\times11.3\)), the three rectangular faces of the upper (triangular prism - like) part (\(A_{u1}=(12 + 12+16)\times20\)) and the two rectangular faces of the lower part (assuming it's a rectangular prism attached, but if we consider the correct formula:
The surface area \(S\) of the composite solid:
The two triangular faces: \(A_{t}=16\times11.3 = 180.8\)
The three lateral faces of the triangular prism: \(A_{l1}=(12 + 12+16)\times20=40\times20 = 800\)
The two faces of the lower rectangular part (assuming it's a rectangular prism and we have to add the two \(16\times12\) faces (if not double - counted). Wait, no:
The correct formula:
The surface area of the composite solid is the sum of the lateral surface area of the triangular prism and the surface area of the rectangular prism with some adjustments.
The lateral surface area of the triangular prism: \(P\times l\), where \(P\) is the perimeter of the triangular base (\(12 + 12+16=40m\)) and \(l = 20m\), so \(40\times20=800m^{2}\)
The area of the two triangular faces: \(2\times\frac{1}{2}\times16\times11.3=180.8m^{2}\)
We also have the two \(16\times12\) faces (assuming the composite solid is made by combining a triangular prism and a rectangular prism in a way that these faces are exposed). So \(A_{3}=2\times16\times12 = 384m^{2}\)

\(S=180.8+800 + 384\)
\(S=1364.8m^{2}\)

Answer:

\(1364.8\)