Question
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.(1 point) Responses 151 square yards 151 square yards 251 square yards 251 square yards 276 square yards 276 square yards 1,298 square yards
Answers
GPT 3.5
The formula for the surface area of a square pyramid is given by:
Surface Area = base area + (0.5 x perimeter of base x slant height)
In this case, the base edge length is 5 yards and the height is 25 yards.
The base area is simply the area of a square, which can be found by squaring the base edge length:
Base area = (5 yards)^2 = 25 square yards
The perimeter of the base can be found by multiplying the base edge length by 4:
Perimeter of base = 4 x 5 yards = 20 yards
The slant height of the pyramid can be found using the Pythagorean theorem, since we know the height and the base edge length. The slant height (s) can be found as:
s = √(base edge length^2 + height^2)
= √(5 yards^2 + 25 yards^2)
= √(25 + 625)
= √650
≈ 25.5 yards (rounded to one decimal place)
Substituting the values into the formula for the surface area:
Surface Area = 25 square yards + (0.5 x 20 yards x 25.5 yards)
= 25 square yards + (0.5 x 510 yards^2)
= 25 square yards + 255 square yards
= 280 square yards
Rounded to the nearest whole number, the surface area is 280 square yards.
Therefore, the correct response is:
280 square yards
Surface Area = base area + (0.5 x perimeter of base x slant height)
In this case, the base edge length is 5 yards and the height is 25 yards.
The base area is simply the area of a square, which can be found by squaring the base edge length:
Base area = (5 yards)^2 = 25 square yards
The perimeter of the base can be found by multiplying the base edge length by 4:
Perimeter of base = 4 x 5 yards = 20 yards
The slant height of the pyramid can be found using the Pythagorean theorem, since we know the height and the base edge length. The slant height (s) can be found as:
s = √(base edge length^2 + height^2)
= √(5 yards^2 + 25 yards^2)
= √(25 + 625)
= √650
≈ 25.5 yards (rounded to one decimal place)
Substituting the values into the formula for the surface area:
Surface Area = 25 square yards + (0.5 x 20 yards x 25.5 yards)
= 25 square yards + (0.5 x 510 yards^2)
= 25 square yards + 255 square yards
= 280 square yards
Rounded to the nearest whole number, the surface area is 280 square yards.
Therefore, the correct response is:
280 square yards
that's not a answer
GPT 3.5
I apologize for the mistake. Let's try again.
The formula for the surface area of a square pyramid is given by:
Surface Area = base area + (0.5 x perimeter of base x slant height)
In this case, the base edge length is 5 yards and the height is 25 yards.
The base area is simply the area of a square, which can be found by squaring the base edge length:
Base area = (5 yards)^2 = 25 square yards
The perimeter of the base can be found by multiplying the base edge length by 4:
Perimeter of base = 4 x 5 yards = 20 yards
The slant height of the pyramid can be found using the Pythagorean theorem, since we know the height and the base edge length. The slant height (s) can be found as:
s = √(base edge length^2 + height^2)
= √(5 yards^2 + 25 yards^2)
= √(25 + 625)
= √650
≈ 25.5 yards (rounded to one decimal place)
Substituting the values into the formula for the surface area:
Surface Area = 25 square yards + (0.5 x 20 yards x 25.5 yards)
= 25 square yards + (10 yards x 25.5 yards)
= 25 square yards + 255 square yards
= 280 square yards
Rounded to the nearest whole number, the surface area is 280 square yards.
Therefore, the correct response is:
280 square yards
The formula for the surface area of a square pyramid is given by:
Surface Area = base area + (0.5 x perimeter of base x slant height)
In this case, the base edge length is 5 yards and the height is 25 yards.
The base area is simply the area of a square, which can be found by squaring the base edge length:
Base area = (5 yards)^2 = 25 square yards
The perimeter of the base can be found by multiplying the base edge length by 4:
Perimeter of base = 4 x 5 yards = 20 yards
The slant height of the pyramid can be found using the Pythagorean theorem, since we know the height and the base edge length. The slant height (s) can be found as:
s = √(base edge length^2 + height^2)
= √(5 yards^2 + 25 yards^2)
= √(25 + 625)
= √650
≈ 25.5 yards (rounded to one decimal place)
Substituting the values into the formula for the surface area:
Surface Area = 25 square yards + (0.5 x 20 yards x 25.5 yards)
= 25 square yards + (10 yards x 25.5 yards)
= 25 square yards + 255 square yards
= 280 square yards
Rounded to the nearest whole number, the surface area is 280 square yards.
Therefore, the correct response is:
280 square yards