Final answer:
To calculate the surface area of a pyramid with a square base and slant height, compute the base area, calculate the triangular side area, and add them together. The pyramid with an 8 cm square base and a 12 cm slant height has a surface area of 256 cm².
Step-by-step explanation:
To find the surface area of a pyramid with a square base and a slant height, we will calculate the area of the base and the area of the four triangular sides. The formula for the surface area (SA) of a pyramid is SA = base area + lateral area.
Step 1: Calculate the base area. Since the base is a square with side lengths of 8 centimeters, the base area is 8 cm × 8 cm = 64 cm².
Step 2: Calculate the area of one triangular side. The formula for the area of a triangle is 1/2 × base × height. In this case, the base of each triangle is 8 centimeters (the side of the square base), and the slant height of the pyramid is 12 centimeters. This gives us the area for one triangle: 1/2 × 8 cm × 12 cm = 48 cm².
Step 3: Since there are four triangles, multiply the area of one triangle by 4. This gives us the total lateral area: 48 cm² × 4 = 192 cm².
Step 4: Add the base area to the total lateral area to find the total surface area: 64 cm² + 192 cm² = 256 cm².
Therefore, the surface area of the pyramid is 256 cm².