Answer:
998 cm²
Explanation:
You want the surface area of the L-shaped prism shown.
Area
The total surface area of the prism will be the sum of the areas of the L-shaped bases and the areas of the rectangular faces.
Base area
Each L-shaped base is a 17 cm by 18 cm rectangle with a cutout that is (17-13) = 4 cm high and (18 -5) = 13 cm wide. Then the area of one base is ...
17·18 -4·13 . . . . . . area of one of two bases
Lateral area
The lateral area of the prism is the product of the perimeter of the base, and the height of the prism (distance between bases). That will be ...
2(17 +18)(7)
Total area
Then the total surface area will be that of the two bases, together with the lateral area:
2(17·18 -4·13) +2(7)(17 +18)
= 2(17·17 -4·13 +7(17 +18)) = 998 . . . . square centimeters
The surface area of the prism is 998 cm².
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Additional comment
The perimeter of the base is the sum of its horizontal boundaries and its vertical boundaries. The sum of the top boundaries is the same as the bottom boundary. Likewise, the sum of left-side boundaries is the same as the right-side boundary. Hence we can treat the perimeter as we would the perimeter of a rectangle with the same overall dimensions.
The area of the base can be computed as the difference of rectangles (as we did), the sum of rectangles, the sum of trapezoids, or other sums. We like to find the simplest decomposition that will give the correct area.
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