Use the formula for the surface area of a square pyramid to find the surface area if the base edge length is 5 yards and height 25 yards. Round to the nearest whole number
The formula for the surface area of a square pyramid is given by:
Surface Area = base area + (1/2) * perimeter of base * slant height
First, let's calculate the base area:
The base of the pyramid is a square, and the formula for the area of a square is given by:
Area = length of side * length of side
Base Area = 5 yards * 5 yards = 25 square yards
Next, let's calculate the perimeter of the base:
The perimeter of a square is given by:
Perimeter = 4 * length of side
Perimeter of Base = 4 * 5 yards = 20 yards
Finally, let's calculate the slant height:
The slant height can be found using the Pythagorean theorem along with the height and half the length of the base. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Slant Height = sqrt(height^2 + (0.5 * base length)^2)
Slant Height = sqrt(25 yards^2 + (0.5 * 5 yards)^2)
Slant Height = sqrt(625 yards^2 + 6.25 yards^2)
Slant Height = sqrt(631.25 yards^2) ≈ 25.12 yards
Now, let's use the formula to calculate the surface area:
Surface Area = base area + (1/2) * perimeter of base * slant height
Surface Area = 25 square yards + (1/2) * 20 yards * 25.12 yards ≈ 25 square yards + 250.5 square yards ≈ 275.5 square yards
Therefore, the surface area of the square pyramid, rounded to the nearest whole number, is approximately 276 square yards.
To find the surface area of a square pyramid, you can use the formula:
Surface Area = Base Area + (0.5 x Perimeter of Base x Slant Height)
First, let's calculate the base area. Since the base of the square pyramid is a square, we can use the formula for the area of a square:
Base Area = side length x side length
Given that the base edge length is 5 yards, the base area is:
Base Area = 5 yards x 5 yards = 25 square yards
Next, let's calculate the perimeter of the base. Since the base is a square, all sides are equal in length. Therefore, the perimeter can be calculated by multiplying the side length by 4:
Perimeter of Base = side length x 4
Perimeter of Base = 5 yards x 4 = 20 yards
Finally, we need to calculate the slant height. For a square pyramid, the slant height can be found using the Pythagorean theorem:
Slant Height = √(height^2 + (0.5 x side length)^2)
Given that the height is 25 yards and the side length is 5 yards, we can calculate the slant height as follows:
Slant Height = √(25^2 + (0.5 x 5)^2)
Slant Height = √(625 + 6.25)
Slant Height = √631.25 ≈ 25.13 yards
Now we can calculate the surface area of the square pyramid:
Surface Area = Base Area + (0.5 x Perimeter of Base x Slant Height)
Surface Area = 25 square yards + (0.5 x 20 yards x 25.13 yards)
Surface Area = 25 square yards + (0.5 x 502.6 square yards)
Surface Area ≈ 25 square yards + 251.3 square yards
Surface Area ≈ 276.3 square yards
Rounded to the nearest whole number, the surface area of the square pyramid is approximately 276 square yards.