Find the surface area of a rectangular pyramid with these measurements: l = 8yd , w = 4
yd., and h = 2yd (1 point)
O 43.31yd .^ 2
O 55.55yd .^ 2
O 72.52yd .^ 2
O 66yd .^ 2
To find the surface area of a rectangular pyramid, we need to calculate the area of each face and then add them together.
The base of the pyramid is a rectangle with length 8 yards and width 4 yards, so the area of the base is 8 * 4 = 32 square yards.
Each of the four triangular faces of the pyramid has a base equal to the width of the rectangle (4 yards) and a height equal to the height of the pyramid (2 yards). Therefore, the area of each triangular face is (1/2) * 4 * 2 = 4 square yards.
In total, the surface area of the pyramid is 32 + 4 + 4 + 4 + 4 = 48 square yards.
Therefore, the correct answer is "O 48yd .^ 2".
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)
O 151 square yards
276 square yards
O 1,298 square yards
O 251 square yards
The surface area of a square pyramid can be calculated using the formula:
Surface Area = base area + (0.5 × perimeter of base × slant height)
The base of the pyramid is a square with an edge length of 5 yards, so the base area is 5 * 5 = 25 square yards.
To calculate the slant height, we can use the Pythagorean theorem. The slant height is the hypotenuse of a right triangle formed by one side of the square base and the height of the pyramid. The height is given as 25 yards.
By applying the Pythagorean theorem, we can find the slant height:
Slant height = √(1/2 * 5^2 + 25^2) = √(1/2 * 25 + 625) = √(287.5) ≈ 16.96 yards
Next, we need to calculate the perimeter of the base, which is the sum of all four sides of the square:
Perimeter of base = 4 * 5 = 20 yards
Finally, we can find the surface area using the formula:
Surface Area = 25 + (0.5 * 20 * 16.96) ≈ 134 + 169.6 ≈ 303.6 square yards
Rounding to the nearest whole number, the surface area is approximately 304 square yards.
Therefore, the correct answer is "276 square yards".
What is the surface area of a square pyramid where the base edge is 8 ft. and the slant height is 16 ft.? (1 point)
O 320ft .^ 2
O 512ft .^ 2
O 256ft .^ 2
O 128f * t ^ 2
The surface area of a square pyramid can be calculated using the formula:
Surface Area = base area + (0.5 × perimeter of base × slant height)
The base of the pyramid is a square with an edge length of 8 ft, so the base area is 8 * 8 = 64 square ft.
The slant height is given as 16 ft.
Next, we need to calculate the perimeter of the base, which is the sum of all four sides of the square:
Perimeter of base = 4 * 8 = 32 ft
Finally, we can find the surface area using the formula:
Surface Area = 64 + (0.5 * 32 * 16) = 64 + 256 = 320 square ft
Therefore, the correct answer is "O 320ft .^ 2".
A pastry chef is creating a chocolate dessert in the shape of a triangular pyramid. The pyramid has a base of 5 in, the height of the base is 4.3 in., and the slant height is 6 in. Use the correct formula to find the surface area of the chocolate pyramid. (1 point)
O 47.25i * n ^ 2
O 52.25 ln.^ 2
O 58.25in .^ 2
O 55.75 ln.^ 2
The correct formula to find the surface area of a triangular pyramid is:
Surface Area = base area + (0.5 × perimeter of base × slant height)
The base of the pyramid is a triangle with a base length of 5 inches and a height of 4.3 inches, so the base area is (1/2) * 5 * 4.3 = 10.75 square inches.
To calculate the perimeter of the base, we need to find the sum of all three sides of the triangle. However, the measurements provided do not give us the lengths of the other two sides. Without that information, we cannot accurately calculate the perimeter or the surface area of the pyramid.
Therefore, we cannot determine the exact surface area of the chocolate pyramid with the given information.