Question

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what is the surface area of this composite solid?
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ft²
(image of composite solid with dimensions: triangular part with 5 ft, 3 ft, rectangular part with 8 ft, 10 ft, 4 ft, 5 ft)

Explanation:

Step1: Identify composite parts

The solid is a rectangular prism + triangular prism (roof).

Step2: Calculate base prism surface area (excluding top)

Base prism: length=10ft, width=8ft, height=4ft.
Lateral surface area: $2*(10*4 + 8*4) = 2*(40+32)=144$ ft².
Bottom area: $10*8=80$ ft².
Total base (excl top): $144+80=224$ ft².

Step3: Calculate triangular prism roof area

Roof: triangular base (base=8ft, height=3ft) × length=10ft.
Two triangular faces: $2*(0.5*8*3)=24$ ft².
Two rectangular faces: $2*(5*10)=100$ ft².
Total roof: $24+100=124$ ft².

Step4: Add base and roof areas

Total surface area: $224 + 124 = 348$ ft².

Answer:

348