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 the height is 25 yards. Round to the nearest whole number.
The formula for the surface area of a square pyramid is given by:
SA = base area + (0.5 x base perimeter x slant height)
The base area is equal to the base edge length squared, so in this case, it is 5 yards squared:
base area = 5^2 = 25 square yards
The base perimeter is equal to 4 times the base edge length, so in this case, it is 4 x 5 = 20 yards.
The slant height can be found using the Pythagorean theorem. Since the base of the pyramid is a square, the height forms the hypotenuse of a right triangle with two legs of length 5 yards each. Therefore, we have:
height^2 = (leg1^2) + (leg2^2)
25^2 = 5^2 + leg2^2
625 = 25 + leg2^2
leg2^2 = 625 - 25
leg2^2 = 600
leg2 ≈ √600
leg2 ≈ 24.49
Now, we can substitute these values into the formula to find the surface area:
SA = 25 + (0.5 x 20 x 24.49)
SA = 25 + (0.5 x 20 x 24.49)
SA = 25 + 12.245
SA ≈ 37.245
Rounding to the nearest whole number, the surface area of the square pyramid is approximately 37 square yards.
that isnt an answer option
I apologize for the mistake. Rounding to the nearest whole number, the surface area of the square pyramid is 37 square yards. It seems that there may be a discrepancy between the provided options and the correct answer.
To find the surface area of a square pyramid, we can use the following formula:
Surface Area = Base Area + (0.5 × Perimeter of Base × Slant Height)
First, let's calculate the base area. Since the base is a square, we can use the formula for the area of a square:
Base Area = (Side Length)^2
Given that the base edge length is 5 yards, we can plug it into the formula:
Base Area = 5^2
Base Area = 25 square yards
Next, let's calculate the slant height. The slant height is the distance from the apex (top) of the pyramid to any of the corners of the base. In this case, we can consider the height as the slant height since the height of the pyramid is perpendicular to the base. Therefore, the slant height is 25 yards.
Now, let's calculate the perimeter of the base. Since the base is a square, all four sides have the same length, which is 5 yards.
Perimeter of Base = 4 × Side Length
Perimeter of Base = 4 × 5
Perimeter of Base = 20 yards
Now let's substitute the values into the surface area formula:
Surface Area = 25 + (0.5 × 20 × 25)
Surface Area = 25 + (0.5 × 500)
Surface Area = 25 + 250
Surface Area ≈ 275
Therefore, the surface area of the square pyramid is approximately 275 square yards.