Final answer:
To find the surface area of a square pyramid, use the formula: s = 1/2 pl + b. Substitute the values for the perimeter of the base, slant height, and area of the base, which can be found using the Pythagorean theorem for the triangular faces.
Step-by-step explanation:
To find the surface area of the square pyramid, we can use the formula given: s = 1/2 pl + b. In this formula, p is the perimeter of the base, l is the slant height, and b is the area of the base. For a square pyramid, the base is a square, so the perimeter of the base would be 4 times the length of one side of the square. To find the slant height, you can use the Pythagorean theorem by considering one of the triangular faces of the pyramid as a right triangle.
Let's say the length of one side of the base square is 'a', then the perimeter of the base would be 4a. Let's say the slant height is 'l', then we can use the Pythagorean theorem: l² = a² + (a/2)².
Once we have the perimeter of the base (4a), the slant height (l), and the area of the base (a²), we can substitute these values into the formula: s = 1/2 (4a)l + a². Simplify the expression, and you will get the surface area of the square pyramid.
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