Find the surface area of a square pyramid with side length 3 cm and slant height 5 cm.
To find the surface area of a square pyramid, we need to find the area of the base and the area of the four triangular faces.
1. The area of the base (which is a square) is side length squared:
Area of base = 3 cm x 3 cm = 9 cm^2
2. To find the area of one of the triangular faces, we can use the formula:
Area of triangle = 0.5 x base x height
The base of the triangle (which is also the side length of the square base) is 3 cm and the height is the slant height of 5 cm. We have:
Area of triangle = 0.5 x 3 cm x 5 cm = 7.5 cm^2
Since the pyramid has 4 triangular faces, the total area of the 4 triangular faces is:
Total area of 4 triangular faces = 4 x 7.5 cm^2 = 30 cm^2
Therefore, the total surface area of the square pyramid is:
Surface area = Area of base + Total area of 4 triangular faces
Surface area = 9 cm^2 + 30 cm^2 = 39 cm^2
So, the surface area of the square pyramid is 39 square centimeters.