The surface area of a rectangular pyramid can be found by calculating the area of the base and the areas of the four triangular faces.
The area of the base is equal to the length multiplied by the width, which in this case is 8 yd. * 4 yd. = 32 yd^2.
The area of each triangular face can be calculated using the formula A = 1/2 * base * height, where the base is the length of the rectangular base and the height is the height of the pyramid.
The area of each triangular face is equal to 1/2 * 8 yd. * 2 yd. = 8 yd^2.
So the total surface area of the pyramid is 32 yd^2 (base) + 4 * 8 yd^2 (triangular faces) = 32 yd^2 + 32 yd^2 = 64 yd^2.
The correct answer is not listed, as the closest option is D. 66 yd^2, which is not the exact surface area of the given measurements.
Find the surface area of a rectangular pyramid with these measurements: l = 8 yd., w = 4 yd., and h = 2 yd.
A. 43.31 yd.^2
B. 55.55 yd.^2
C. 72.52 yd.^2
D. 66 yd.^2
11 answers
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.
A. 1,298 square yards
B. 251 square yards
C. 151 square yards
D. 276 square yards
A. 1,298 square yards
B. 251 square yards
C. 151 square yards
D. 276 square yards
The surface area of a square pyramid can be found using the formula:
Surface Area = base area + (1/2 * perimeter * slant height)
The base area of a square pyramid is equal to the length of one side squared, so in this case, it is 5 yards * 5 yards = 25 square yards.
To calculate the slant height, we can use the Pythagorean theorem. The slant height, in this case, will be the square root of the sum of half the base length squared plus the height squared.
Slant height = √((1/2 * 5 yd)^2 + 25 yd^2)
Slant height = √(6.25 yd^2 + 25 yd^2)
Slant height = √(31.25 yd^2)
Slant height ≈ 5.59 yd
Now we can substitute the values into the surface area formula:
Surface Area = 25 yd^2 + (1/2 * 4 * 5 yd * 5.59 yd)
Surface Area ≈ 25 yd^2 + (1/2 * 4 * 27.95 yd^2)
Surface Area ≈ 25 yd^2 + 55.9 yd^2
Surface Area ≈ 80.9 yd^2
Rounding to the nearest whole number, the surface area is approximately 81 square yards.
The correct answer is not listed, as the closest option is B. 251 square yards, which is not the surface area of the given measurements.
Surface Area = base area + (1/2 * perimeter * slant height)
The base area of a square pyramid is equal to the length of one side squared, so in this case, it is 5 yards * 5 yards = 25 square yards.
To calculate the slant height, we can use the Pythagorean theorem. The slant height, in this case, will be the square root of the sum of half the base length squared plus the height squared.
Slant height = √((1/2 * 5 yd)^2 + 25 yd^2)
Slant height = √(6.25 yd^2 + 25 yd^2)
Slant height = √(31.25 yd^2)
Slant height ≈ 5.59 yd
Now we can substitute the values into the surface area formula:
Surface Area = 25 yd^2 + (1/2 * 4 * 5 yd * 5.59 yd)
Surface Area ≈ 25 yd^2 + (1/2 * 4 * 27.95 yd^2)
Surface Area ≈ 25 yd^2 + 55.9 yd^2
Surface Area ≈ 80.9 yd^2
Rounding to the nearest whole number, the surface area is approximately 81 square yards.
The correct answer is not listed, as the closest option is B. 251 square yards, which is not the surface area of the given measurements.
What is the surface area of a square pyramid where the base edge is 8 ft. and the slant height is 16.?
A. 128 ft.^2
B. 512 ft.^2
C. 320 ft.^2
D. 256 ft.^2
A. 128 ft.^2
B. 512 ft.^2
C. 320 ft.^2
D. 256 ft.^2
The surface area of a square pyramid can be found using the formula:
Surface Area = base area + (1/2 * perimeter * slant height)
The base area of a square pyramid is equal to the length of one side squared, so in this case, it is 8 ft * 8 ft = 64 square ft.
The slant height is given as 16 ft.
Now we can substitute the values into the surface area formula:
Surface Area = 64 ft^2 + (1/2 * 4 * 8 ft * 16 ft)
Surface Area = 64 ft^2 + (1/2 * 4 * 128 ft^2)
Surface Area = 64 ft^2 + 256 ft^2
Surface Area = 320 ft^2
The surface area of the given square pyramid is 320 square feet.
The correct answer is C. 320 ft^2.
Surface Area = base area + (1/2 * perimeter * slant height)
The base area of a square pyramid is equal to the length of one side squared, so in this case, it is 8 ft * 8 ft = 64 square ft.
The slant height is given as 16 ft.
Now we can substitute the values into the surface area formula:
Surface Area = 64 ft^2 + (1/2 * 4 * 8 ft * 16 ft)
Surface Area = 64 ft^2 + (1/2 * 4 * 128 ft^2)
Surface Area = 64 ft^2 + 256 ft^2
Surface Area = 320 ft^2
The surface area of the given square pyramid is 320 square feet.
The correct answer is C. 320 ft^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.
A. 58.25 in.^2
B. 52.25 in.^2
C. 55.75 in.^2
D. 47.25 in.^2
A. 58.25 in.^2
B. 52.25 in.^2
C. 55.75 in.^2
D. 47.25 in.^2
The formula for the surface area of a triangular pyramid is given by:
Surface Area = 1/2 * base perimeter * slant height + base area
First, let's calculate the base area. The base of the pyramid is a triangle with a base length of 5 in and a height of 4.3 in. Using the formula for the area of a triangle, we have:
Base Area = (1/2) * base * height
Base Area = (1/2) * 5 in * 4.3 in
Base Area ≈ 10.75 in^2
Next, we need to calculate the base perimeter. Since it is a triangle, the perimeter is equal to the sum of the lengths of the three sides. In this case, all sides have a length of 5 in, so the base perimeter is:
Base Perimeter = 3 * 5 in
Base Perimeter = 15 in
Now we can substitute the values into the formula for the surface area:
Surface Area = 1/2 * 15 in * 6 in + 10.75 in^2
Surface Area = 7.5 in * 6 in + 10.75 in^2
Surface Area = 45 in^2 + 10.75 in^2
Surface Area ≈ 55.75 in^2
The surface area of the chocolate pyramid is approximately 55.75 square inches.
The correct answer is C. 55.75 in^2.
Surface Area = 1/2 * base perimeter * slant height + base area
First, let's calculate the base area. The base of the pyramid is a triangle with a base length of 5 in and a height of 4.3 in. Using the formula for the area of a triangle, we have:
Base Area = (1/2) * base * height
Base Area = (1/2) * 5 in * 4.3 in
Base Area ≈ 10.75 in^2
Next, we need to calculate the base perimeter. Since it is a triangle, the perimeter is equal to the sum of the lengths of the three sides. In this case, all sides have a length of 5 in, so the base perimeter is:
Base Perimeter = 3 * 5 in
Base Perimeter = 15 in
Now we can substitute the values into the formula for the surface area:
Surface Area = 1/2 * 15 in * 6 in + 10.75 in^2
Surface Area = 7.5 in * 6 in + 10.75 in^2
Surface Area = 45 in^2 + 10.75 in^2
Surface Area ≈ 55.75 in^2
The surface area of the chocolate pyramid is approximately 55.75 square inches.
The correct answer is C. 55.75 in^2.
When creating the formula for surface area of a triangular pyramid (S A = 1/2 ab + 3 (1/2lb)), what formula is being used?
A. volume
B. perimeter
C. area of a triangle
D. area of a square
A. volume
B. perimeter
C. area of a triangle
D. area of a square
The formula being used for the surface area of a triangular pyramid (SA = 1/2 ab + 3 (1/2lb)) is a combination of two formulas: the formula for the area of a triangle (1/2 base times height) and the formula for the perimeter of a triangle (the sum of the lengths of the three sides of a triangle).
Therefore, the correct answer would be a combination of the formulas C. area of a triangle and B. perimeter.
Therefore, the correct answer would be a combination of the formulas C. area of a triangle and B. perimeter.
only one is needed
Apologies for the confusion. In that case, the formula being used for the surface area of a triangular pyramid (SA = 1/2 ab + 3 (1/2lb)) is specifically the formula for the area of a triangle (1/2 base times height).
Therefore, the correct answer is C. area of a triangle. The use of the perimeter is not required in this particular formula for finding the surface area of a triangular pyramid.
Therefore, the correct answer is C. area of a triangle. The use of the perimeter is not required in this particular formula for finding the surface area of a triangular pyramid.