Final answer:
The surface area of the pyramid is 340 cm².
Step-by-step explanation:
To find the surface area of the pyramid, we need to calculate the area of the base and the area of the triangular faces. The base is a square with side lengths of 10 centimeters, so we can use the formula for the area of a square:
Area = side length x side length.
In this case, the area of the base is 10 cm x 10 cm = 100 cm².
The triangular faces have a slant height of 12 centimeters.
Each face is an isosceles triangle, so we can use the formula for the area of a triangle:
Area = 1/2 x base x height.
In this case, the base is 10 centimeters (the same as the side length of the square base) and the height is 12 centimeters.
So the area of each triangular face is
1/2 x 10 cm x 12 cm = 60 cm².
Since there are 4 triangular faces, the total area of the triangular faces is
4 x 60 cm² = 240 cm².
Finally, to calculate the surface area of the pyramid, we add the area of the base to the total area of the triangular faces:
Surface Area = Base Area + Triangular Face Area.
In this case, the surface area of the pyramid is 100 cm² + 240 cm² = 340 cm².