To find the surface area of a pyramid, we need to calculate the area of the base and the area of the lateral faces.
Base area:
The base of the pyramid is a square, so we can use the formula for the area of a square to find the base area.
Area of square base = width^2 = 6.7^2 = 45.29 sq m
Lateral area:
To find the lateral area, we need to find the slant height of the pyramid. We can use the Pythagorean theorem to find the slant height given the height and the base diagonal.
a^2 + b^2 = c^2, where c is the slant height, a is the height of the pyramid (9.8 m), and b is half the base width (6.7/2 = 3.35 m)
c^2 = a^2 + b^2 = 9.8^2 + 3.35^2 = 96.04 + 11.25 = 107.29
c = √107.29 = 10.34 m
Now that we have the slant height, we can use the formula for the lateral area of a pyramid to find the lateral area:
Lateral area = 1/2 * perimeter * slant height
Perimeter of base = 4 * width = 4 * 6.7 = 26.8 m
Lateral area = 1/2 * 26.8 * 10.34 = 138.532 sq m
Total surface area:
The total surface area of the pyramid is the sum of the base area and the lateral area:
Surface area = base area + lateral area = 45.29 + 138.532 = 183.822 sq m
So the surface area of the pyramid is approximately 183.82 sq m to the nearest thousandth.