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Find the surface area of a composite solid with the following dimensions:

Base length = 4 m
Base width = 4 m
Height = 5 m
The solid also has an additional rectangular section attached with dimensions:

Length = 4 m
Width = 4 m

A. 120 m²
B. 136 m²
C. 152 m²
D. 104 m²

User Tuviah
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1 Answer

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Final answer:

The surface area of the composite solid is calculated by adding the surface area of the base prism and the additional rectangle, resulting in 120m² which corresponds to option A.

Step-by-step explanation:

The question is asking to find the surface area of a composite solid which is the total area of all the surfaces of the solid. Since the solid consists of a base rectangular prism and an additional attached rectangle, we must calculate the surface area of each and sum them. For the base prism with dimensions 4m x 4m x 5m, the surface area is the sum of the areas of all six faces (2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height). So, we calculate 2(4m × 4m) + 2(4m × 5m) + 2(4m × 4m), which equals 32m² + 40m² + 32m² = 104m². The additional rectangular section is a flat surface, thus its surface area is simply its length times its width (lw), which is 4m × 4m = 16m². Adding up both these areas gives us 104m² + 16m² = 120m², which is option A.

User Npatel
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