Answer: 136.58 square yards
Explanation:
Since the pyramid has an equal side lengths base, we can assume it's a square pyramid.
The formula for the surface area of a square pyramid is given by:
Surface area = base area + (0.5 × perimeter of base × slant height)
We need to find the base area and the slant height first.
Given that the side length of the base is 11.4 yards, the base area can be calculated as:
Base area = (side length)^2 = 11.4^2 = 129.96 square yards
To find the slant height, we need to use the Pythagorean theorem:
(0.5 × diagonal)^2 = (side length)^2 + (height)^2
where the diagonal is the hypotenuse of the base, which can be calculated as:
diagonal = sqrt(2) × side length = sqrt(2) × 11.4 = 16.1224 yards (rounded to 4 decimal places)
Now we can find the height of the pyramid:
(0.5 × diagonal)^2 = (side length)^2 + (height)^2
(0.5 × 16.1224)^2 = 11.4^2 + (height)^2
130.043 = 129.96 + (height)^2
(height)^2 = 0.0839
height = sqrt(0.0839) = 0.2895 yards (rounded to 4 decimal places)
Now we can calculate the surface area:
Surface area = base area + (0.5 × perimeter of base × slant height)
Surface area = 129.96 + (0.5 × 4 × 11.4 × 0.2895)
Surface area = 129.96 + 6.62364
Surface area = 136.58364 square yards (rounded to 2 decimal places)
Therefore, the surface area of the pyramid is approximately 136.58 square yards.