Find the surface area of a square pyramid with side length 4 yd and slant height 6 yd.
To find the surface area of a square pyramid, we need to calculate the area of the base and the area of the four triangular faces.
The base of the pyramid is a square with side length 4 yards. The area of the base can be calculated as:
Area of base = side length squared
Area of base = 4^2
Area of base = 16 sq yd
Now, we need to calculate the area of the four triangular faces. Each triangular face is an isosceles triangle with a base equal to the side length of the square base (4 yd) and a slant height of 6 yards.
To find the area of one triangular face, we can use the formula for the area of a triangle:
Area of triangle = (1/2) * base * height
Area of triangle = (1/2) * 4 * 6
Area of triangle = 12 sq yd
Since there are 4 triangular faces, the total area of the four triangular faces is:
Total area of triangular faces = 4 * Area of triangle
Total area of triangular faces = 4 * 12
Total area of triangular faces = 48 sq yd
Now, we can find the total surface area of the square pyramid by adding the area of the base and the area of the four triangular faces:
Total surface area = Area of base + Total area of triangular faces
Total surface area = 16 + 48
Total surface area = 64 sq yd
Therefore, the surface area of the square pyramid is 64 square yards.