Answer:
Explanation:
To find the surface area of a pyramid, we need to add together the area of the base and the area of the four triangular faces.
First, we can find the area of the base of the pyramid by using the formula for the area of a square:
Area of base = side x side
Since the side lengths of the base are equal, we can use any one of them. Let's use 9 ft:
Area of base = 9 ft x 9 ft
Area of base = 81 square feet
Next, we need to find the area of each triangular face. To do this, we can use the formula for the area of a triangle:
Area of triangle = (1/2) x base x height
Since the pyramid is regular, each triangular face will have the same base and height. To find the height, we can use the Pythagorean theorem. Let's call the height "h":
h^2 = (12/2)^2 - (9/2)^2
h^2 = 36 - 20.25
h^2 = 15.75
h = square root (15.75)
h ≈ 3.97 ft
Now we can find the area of each triangular face:
Area of triangle = (1/2) x base x height
Area of triangle = (1/2) x 9 ft x 3.97 ft
Area of triangle ≈ 17.8 square feet
Finally, we can find the total surface area of the pyramid by adding together the area of the base and the area of the four triangular faces:
Total surface area = area of base + area of four triangles
Total surface area = 81 square feet + 4 x 17.8 square feet
Total surface area ≈ 143.2 square feet
Therefore, the surface area of the pyramid is approximately 143.2 square feet.