Find the surface area of the given pyramid
Bottles 7yr
Side 9yd inside 7yd
To find the surface area of the pyramid, we first need to calculate the lateral area and then add the area of the base.
The lateral area of a pyramid can be calculated using the formula:
Lateral Area = (Perimeter of base * slant height) / 2
First, let's calculate the perimeter of the base:
Perimeter = 4 * 7 yd = 28 yd
Next, we need to calculate the slant height, which can be found using the Pythagorean theorem:
slant height = sqrt(9^2 + 7^2) = sqrt(81 + 49) = sqrt(130) ≈ 11.40 yd
Now, we can calculate the lateral area:
Lateral Area = (28 yd * 11.40 yd) / 2 ≈ 159.60 yd^2
Next, we need to calculate the area of the base, which is a square with side length 7 yd:
Area of base = 7 yd * 7 yd = 49 yd^2
Now, we can find the total surface area by adding the lateral area and the area of the base:
Surface Area = Lateral Area + 2 * Area of base
Surface Area = 159.60 yd^2 + 2 * 49 yd^2
Surface Area = 159.60 yd^2 + 98 yd^2
Surface Area = 257.60 yd^2
Therefore, the surface area of the given pyramid is 257.60 square yards.