To find the surface area of the square pyramid, we need to calculate the area of the base and the areas of the four triangular faces.
-
Area of the Base: The base of the pyramid is a square with side length \( s = 6 \) meters. The area \( A_{\text{base}} \) of the square base can be calculated using the formula: \[ A_{\text{base}} = s^2 = 6^2 = 36 \text{ m}^2 \]
-
Area of the Triangular Faces: Each triangular face has a base equal to the side of the square base, which is \( b = 6 \) meters, and a height \( h = 9 \) meters (the height of each triangular face). The area \( A_{\text{triangle}} \) of one triangle can be calculated using the formula: \[ A_{\text{triangle}} = \frac{1}{2} \times b \times h = \frac{1}{2} \times 6 \times 9 = 27 \text{ m}^2 \] Since there are 4 triangular faces, the total area for all triangular faces is: \[ A_{\text{triangles}} = 4 \times A_{\text{triangle}} = 4 \times 27 = 108 \text{ m}^2 \]
-
Total Surface Area: The total surface area \( A_{\text{total}} \) of the pyramid is the sum of the area of the base and the total area of the triangular faces: \[ A_{\text{total}} = A_{\text{base}} + A_{\text{triangles}} = 36 + 108 = 144 \text{ m}^2 \]
Thus, the surface area of the square pyramid is \( \boxed{144} \) m².