Final answer:
The surface area of the square pyramid is 15.32ft².
Step-by-step explanation:
To find the surface area of a square pyramid, you need to calculate the area of the base and the lateral faces. The base is a square, so the area of the base is the square of the side length: 2ft x 2ft = 4ft². The lateral faces are triangles, and the slant height is the height of each triangle. Since the slant height is 3ft and the base side length is 2ft, you can use the Pythagorean theorem to calculate the height of each triangle: h = sqrt(3² - 1²) = sqrt(8) = 2.83ft. The area of each triangle is then 1/2 x base x height, where the base is the side length of the pyramid: (1/2) x 2ft x 2.83ft = 2.83ft². Since there are 4 triangles, the total area of the lateral faces is: 4 x 2.83ft² = 11.32ft². Finally, to find the surface area, you add the area of the base and the area of the lateral faces: 4ft² + 11.32ft² = 15.32ft².
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