Use the formula for the surface area of a square pyramid to solve for the slant height if the length of the base is 40 in and SA equals 2,800 in.
The formula for the surface area of a square pyramid is given by:
SA = (1/2) × base perimeter × slant height + base area
In this case, the base length is 40 in and the surface area is 2800 in². Let's assume the slant height as "s".
The base perimeter of a square is given by: P = 4 × length of a side
In this case, the base perimeter is P = 4 × 40 = 160 in.
Now, we can substitute these values in the formula and solve for the slant height:
2800 = (1/2) × 160 × s + (40 × 40)
2800 = 80s + 1600
80s = 2800 - 1600
80s = 1200
s = 1200 / 80
s = 15
Therefore, the slant height is 15 in.
The formula for the surface area of a square pyramid is given by:
SA = (1/2) × base perimeter × slant height + base area
In this case, the base length is 40 in and the surface area is 2800 in². Let's assume the slant height as "s".
The base perimeter of a square is given by: P = 4 × length of a side
In this case, the base perimeter is P = 4 × 40 = 160 in.
Now, we can substitute these values in the formula and solve for the slant height:
2800 = (1/2) × 160 × s + (40 × 40)
2800 = 80s + 1600 + 1600
2800 - 3200 = 80s
-400 = 80s
s = -400 / 80
s = -5
Therefore, the slant height is -5 in. However, a slant height cannot be negative. This indicates that there may be an error in the given information or calculation, or the square pyramid may not exist. Please double-check the measurements and try again.
Use the formula for the surface area of a square pyramid to solve for the slant height if the length of the base is 40 in and SA equals 2,800 in^2.
What is the surface area of a square pyramid where the base edge is 8ft. and the slant height is 16 ft.?
To find the surface area of a square pyramid, we can use the following formula:
SA = 2 × base area + base edge × slant height
First, we need to calculate the base area. The area of a square base is given by:
Base area = length of side × length of side
In this case, the base edge is 8 ft, so the base area is:
Base area = 8 ft × 8 ft = 64 ft²
Now, we can substitute the values into the surface area formula:
SA = 2 × 64 ft² + 8 ft × 16 ft
SA = 128 ft² + 128 ft
SA = 256 ft²
Therefore, the surface area of the square pyramid is 256 ft².
What is the surface area of a square pyramid where the base edge is 5 yards and the slant height is 25 ft.? Round to the nearest whole number.
To find the surface area of a square pyramid, we can use the following formula:
SA = base area + lateral area
The base area of a square pyramid is given by:
Base area = (base edge)^2
In this case, the base edge is 5 yards, so the base area is:
Base area = (5 yards)^2 = 25 square yards
The lateral area of a square pyramid is given by:
Lateral area = (base edge)(slant height)/2
In this case, the base edge is 5 yards and the slant height is 25 ft. We need to convert the slant height to yards:
25 ft = 25/3 = 8.333... yards (rounded to 3 decimal places)
Now, we can calculate the lateral area:
Lateral area = (5 yards)(8.333... yards)/2 = 20.833... square yards
Finally, we can find the surface area:
SA = 25 square yards + 20.833... square yards ≈ 45.83 square yards
Rounding to the nearest whole number, the surface area of the square pyramid is 46 square yards.
A pastry chef is creating a chocolate desert in the shape of a triangular pyramid. The pyramid has a base of 5 in., the height has a base of 4.3 in., and the slant height is 6 in. Use the correct formula to find the surface area of the chocolate pyramid.
To find the surface area of a triangular pyramid, we can use the following formula:
SA = (base area) + (lateral area)
The base area of a triangular pyramid is given by:
Base area = (1/2) × base × height
In this case, the base is 5 in and the height is 4.3 in. We can substitute these values into the formula:
Base area = (1/2) × 5 in × 4.3 in = 10.75 in²
The lateral area of a triangular pyramid is given by:
Lateral area = (perimeter of base) × (slant height) / 2
In this case, the perimeter of the base of the triangular pyramid is the sum of all three sides, which is 5 in + 5 in + 5 in = 15 in. Let's substitute the values into the formula:
Lateral area = (15 in) × (6 in) / 2 = 45 in²
Now, we can find the surface area by adding the base area and the lateral area:
SA = 10.75 in² + 45 in² = 55.75 in²
Therefore, the surface area of the chocolate pyramid is approximately 55.75 in².
When creating the formula for surface area of a triangular pyramid, what formula is being used?
A. perimeter
B. area of a triangle
C. area of a square
D. volume