Final answer:
To find the total surface area of a pyramid with a square base, calculate the area of the base and the area of the triangular faces. Then, add them together.
Step-by-step explanation:
To find the total surface area of a pyramid, you need to find the area of each face and add them together. In this case, the base of the pyramid is a square with side length 10 cm. The area of the base is 10 cm * 10 cm = 100 cm². The triangular faces of the pyramid can be divided into four congruent triangles. To find the area of one triangle, you can use the formula for the area of a triangle, which is 1/2 * base * height. The base of each triangle is 10 cm (the side length of the base) and the height is the altitude of the pyramid, which is 12 cm. So the area of one triangle is 1/2 * 10 cm * 12 cm = 60 cm². Since there are four triangles, the total area of the triangular faces is 4 * 60 cm² = 240 cm². Finally, to find the total surface area, you add the area of the base and the area of the triangular faces: 100 cm² + 240 cm² = 340 cm².